Galaxy Tab 10.1 doesn't keep wifi connected despite settings My Galaxy Tab 10.1, 16GB Wifi only version, disconnects the WiFi whenever the tablet goes into sleep mode.

I have ensured that I have selected to never sleep in advanced WiFi settings.

I downloaded and experimented with the Wifi Keep Alive and REGPON wifi KeepAlive apps, but they have had no effect.

I even tried rooting the device, and put on this ROM, in hopes that maybe some change would take effect, but it hasn't.

Is this a known issue with the Galaxy Tab 10.1? I've done some Google searching and I've seen other people report it, but most fixes seem to just describe how to go into the advanced settings and enable "never" as an option.

Is there any kind of fix I can apply?

This is a somewhat critical feature for me, as I intend to be able to receive Skype calls, which can't be done if the WiFi disconnects.
In a nutshell: using a static IP is like owning a house.  Having a DHCP lease is like renting, but you may have to move when the lease is up.  Unfortunately, the Tab's implementation is like a renter who leaves, then tries to get back into his old apartment (which in this analogy is a dynamically assigned IP address on your WiFi network) and finds it locked.  Instead of asking for a new lease, it just keeps knocking on the door, never to enter.  In this case, it means that your Tab won't connect to your WiFi network on wake.

The detailed explanation: It looks like Samsung's implementation of DHCP lease renewal is at fault here.  When a device wakes up and then tries to connect to WiFi, it will ask for a DHCP lease (if expired), which also gives it a dynamically assigned IP address.  This works fine when the Tab first connects.  However it looks like it never asks for a new lease and thus new IP address.  Instead it caches the IP address and keeps trying to reuse it.  DHCP is dynamic so it means that any particular device on the network cannot rely on a specific IP.  So eventually the lease will expire and/or the IP address that the Tab is using gets reassigned to another device.  When this happens, your Tab cannot connect to WiFi.

So the solution is to assign static IP until the Tab's implementation of DHCP lease renewal is fixed.

An alternative solution is to root your device.  Then you can manually delete the cached file which contains the stale IP address following the instructions at: http://steve-shaffer.com/2011/02/samsung-galaxy-tab-wifi/ (where I learned about some of these details as well).  This will cause the Tab to renew the DHCP lease properly and live in a brand new and shiny dynamically assigned apartment on your WiFi network.