Can a MacBook Air battery be replaced?
Apple will replace it for $129 US (price varies by country), or you can do it yourself, following iFixit's guide. However iFixit lists a used 2010/2011 MacBook Air battery for $99 US, and if you mess up anything doing the repair, it won't be covered under warranty. If I were you, I'd spend the extra $30 and have Apple do it.
It's also worth noting that Apple has improved battery durability considerably over the past few years (I think ever since they went with the &quot;non-removeable&quot; batteries). From Apple.com:

The built-in battery of your MacBook Pro or MacBook Air is designed to deliver up to 1000 full charge and discharge cycles before it reaches 80 percent of its original capacity.

One &quot;cycle&quot; is a full discharge and recharge - so going from 100% to 0%. Or Going 100% to 50% twice.
For comparison, the older batteries (and to my knowledge, most non-Apple batteries) were rated for 300 cycles. In my experience, the first 300 cycles on my MacBook Pro took about 2 to 3 years of pretty heavy use (you can keep track in the System Information app, under the Power section). 1000 cycles should last the usable life of an Air, unless you're in the 99th percentile of hard use.