Wi-Fi connection randomly disconnects on 2012 MacBook Air
This is a topic I have followed online and in "real life" for several months. Anecdotally, Apple seems to have a wifi problem with the 2012 MacBookAir. I have no firm figures concerning how widespread this situation is, but I know of two other MacBook Air laptops that have displayed this issue: 


the MBA I purchased in hopes that I could use it attached to a
projector as the remote end of a video presentation at a conference I
had to miss for health reasons. I returned the computer one week
later after investing ten or so hours trying to fix dropping WiFi
connections.
my oldest daughter's 2012 12" MBA that she still has and is now connecting more reliably, close to 95%+


The resulting story is long, but reading the full adventure might help to open your eyes to the minutiae that helped me resolve her WiFi nightmare.

Shortly after purchasing the MBA for my daughter, she started complaining of wifi drops, initially at home and then she began experiencing drops everywhere--but not at my office where my AirPort Extreme literally sits on a shelf, three feet above my head. My initial thought focused on signal strength and distance from the router. While attending college she lives at my parents' home. The walls are lathe and plaster and the WiFi access point was at the opposite side of the house. I don't remember the brand, but it could have been a Linksys or DLink, and was only a 2.4GHz wireless-G unit.

While working with my daughter, I started some online research, including Apple Discussion boards. When I saw how many posts and complaints floated around the internet, and how few people had positive response from Genius Bar denizens, I figured that I would need strong documentation if I was going to get anywhere with them.

I worked to document and remedy connection stability on two fronts. 

If you'd rather cut to The Chase and skip the steps that expanded my understanding of the issue, scroll down to the end of my post.

Tracking and replicating problems with her computer


Apple includes WiFi Diagnostics with OS X. Select Open WiFi Diagnostics from the WiFi menu while holding the OPTION key. 
Don't worry about the three options on the main app screen, but first select Wi-Fi Scan from the View menu. 

The channel, width, band, signal and noise are all listed. 
You want the least competition for channels. Change that at the router if needed. 
Signal and Noise are affected by interference from walls, electrical wiring and other environmental issues. 

The larger the gap between the signal and noise represents a better connection.

Much of this information is available on the WiFi menu if you hold the OPTION key while clicking on the menu.
You can get a visual ticker tape for signal/noise by selecting Performance in the Network Utilities window.

Keep a log of approximate time/date, RSSI (signal strength), transmit rate and any important events. 

Don't worry about keeping this log religiously. 
Make a note any time you experience a noticeable change in WiFi speed. 
Note the times you reset the WiFi router.
Every time you have a WiFi drop, be sure to note the event and the signal strength and rate. 
More than dates and strengths, look for patterns. 

At home, WIFI dropped
Logged out and back in
Walked from room
Connected to the DSL WiFi router at dad's house and dropped.
Rebooted laptop
Laptop on table
Lots if static from wind
At library, no WIFI drops
Just rebooted router
At dad's and connected to the Time Capsule. Not dropped.
At hardware store, WIFI dropped

Note any errors the MBA displays.

Unexpected WiFi timeout


If all else fails, you have something to take with you to the Genius Bar or discuss with Apple support that has stronger documentation than "The damn thing doesn't work!"
I also attempted to replicate the WiFi problems with my early-2009 17" MacBook Pro. My laptop remained connected every time we were together and hers dropped the WiFi.


Tracking and replicating problems with the router


General router information...

What make/model is your wireless router?
How old is it?
Are you connecting using 2.4GHz, 5GHz or both?

General site description...

How far away is the router from where you use your MBA?

Create a wireless site survey with NetSpot

It's a free download from the Mac App Store. 
Use the program to draw out a map of where you use your computer (home, office, etc.) including all the interior walls between you and the router. 
You walk around the site, using NetSpot to capture signal strength, noise and other information. 
Post a capture of the results and I'll be happy to help see what might help.



Generally, you'll have better connectivity closer to the router. If you have a clear line of sight to the router, you should have a good signal.

I know my daughter got sick and tired of having WiFi drop, rebooting the router and/or her MBA.

How I finally made things better

I ended up controlling the two variables I could directly manipulate: signal strength and age of WiFi router. In the end, my solution improved internet connectivity throughout my parents' home, benefitting everyone.

I started out replacing the router with another older, non-Apple one I had sitting around my office, possibly an old AirLink. No positive affect. Then I replaced it with a third slightly-newer, non-Apple router. Again, no change. In order to re-connect after a drop, my daughter would walk to the other side of the house and reboot the router every time there was a wireless drop.

I brought a 30' length of CAT-5 from the office so I could position the various router closer to her bedroom. WiFi signal strength and overall quality improved, but she still experienced the drops three or four times a day. I think she would have been happy at this point, but the problem had become personal with me.

As I analyzed everything, I decided to introduce the one element she had not experienced from my office into my daughter's home:


I snagged an AirPort Express from my shop and reconfigured it for her
local network. It replaced the older, non-Apple router that was
there. Unbeknownst to me, we had the AirPort Express plugged into
a power outlet shared with a lamp that was controlled by a wall
switch. My daughter switched off the light when she would leave for
college, and also the router. Quality improved once again, with
signal drops once or twice a day. My parents were starting to get
annoyed by a twisty blue wire running through their home.
We changed the outlet to one with permanent power and after a couple 
of days the signal stabilized and seemed to finally start running
properly. However, my parents were still annoyed by the twisty blue
wire running through their home. I figured I was close enough to a
stable solution that I invested some money in hopes of staunching the
flow of time and phone calls at all hours of the night. Money became 
less important than sleep.
I installed a AirPort Extreme where the DSL modem is located at the
far end of my parents' house, in my dad's office. The Extreme bathes
the office with multichannel 5GHz goodness that links between 300MBs
and 450MBs. This one access point covers that half of the house with
2.4GHz coverage and 150MBs to 270MBs connectivity.
I dragged a CAT6 cable through the hot and dusty attic to a location
near my daughter's bedroom, near the other end of the house. I
attached an AirPort Express at this end which provides a near mirror
of the Extreme.
I bound the 5GHz and 2.4GHz into a single SSID/Network name.
I enabled the Express to extend the Extreme's wireless network,
connecting the two access points for passwords and transparent
passing from one access point to the other as one moves throughout
the house.
Both the AirPorts are powered and connected to the DSL modem 24/7.
While I was at it, I enabled a guest network with a separate
password.




The Chase

I think the 2012 MacBook Air WiFi issue might be because Apple has integrated Intel's more aggressive power-saving modes into the laptop. In a drive to maximize battery life, these new low-power modes change how (and how often) the laptop communicates with the wireless access point.


Apple introduces Intel's deep power states as Power Nap on their latest equipment.
From what I've been able to read on OEMs implementing the new lower
power modes (and we'll group Apple in as just another OEMs), Intel needs
greater control of the various components on the motherboard and has met resistance. 
The price-sensitive business model that drives the Windows world
forces most OEMs to include the lowest-cost subsystems, not
necessarily the latest technology.
Since Apple does not play in the race to the bottom with prices and
profitability, the company often offers newer technology in their
products.
Apple is pushing the limits of throughput vs power consumption with
the 2012 MBA's WiFi subsystems. My 2009 MBP keeps the WiFi powered on
at all times so will never see the problem introduced when mixing an
older router with a newer laptop.
Older routers would see an IP address turning themselves off at
random times...  which then would drop the connection.
The 2012 MBA expects wireless access points to provide a longer time duration
before releasing a connection. 
I found timeout durations in all the older routers' HTML-based
configuration systems, but could not make a change to any of them
from the default values.
When a system that has powered down the WiFi subsystem (even though
the user believes they are still working merrily right along) needs
to ping the Internet, the MBA powers up the "sleeping" WiFi
subsystem, only to discover the wireless access point has terminated
their connection.


Yes, this is a long-winded and overly-detailed story. I spent several hours this afternoon thinking through each element of the plot as I typed the events, and I'm somewhat embarrassed to admit I completely rewrote the ending because of thoughts developed and linked with random memories that I hadn't seen as possibly being interrelated. 

There are many times that my quick, three line answer does not allow me the time to "think with my fingers". Instead of resolving an issue I sloppily (and possibly expensively) slapped a band-aid on the owie. 

I resolved the dropped network issue by replacing the "antiquated" WiFi router with a "modern" one. I just happened to select one manufactured by Apple. 
Either 


increase the time an older router will keep an inactive connection
alive before timeout (which may not be changeable in any given older
router), or
replace it with one that supports Intel's newer power-saving states.