I have this problem as well. I have only an Extreme and an Express. Many people suggest the solution is to set up the ethernet (hardwiare) the Express to the Extreme. Does this not defeat the point of "Air" play? After all, we are in a wireless world. And, of course, many of us do not have an ethernet connection available near our Express (which in my case is attached to my stereo in the living room).
I bought the Express to extend my network and get a better signal at the far side of the house. Frankly, it was rather ineffective. The Express is half-way between my computer at the far side of the house to my Extreme on the other side. When my computer found the Express, it did not improve my overall download speeds.
However, my wife like the idea of the Airplay feature so much (streaming from Ipad to the stereo), which was located near that half-way point, we decided to keep it anyway.
In our case, using Airplay from the computer to the Express works flawlessly. Using Airplay from the iPad to the Express also works flawlessly. However, using Airply from the iPod Touch to the Express cuts out every minute or so.
I am still trying to find the solution! Yes, I can use the "Remote" app so that my Ipod controls my computer and the computer sends the signal to the Express via Airplay. That works fine, as long as my computer is turned on and iTunes is turned on.
Yes, I can set up the ethernet so my Express talks to my Extreme hardwired. Not my preferred solution!
I don't think there is a "solution" to this problem. Apple needs to fix it. Sorry I can't provide a solution, after reading all these comments, suggestions, and trying various suggestions, I have come to the conclusion that the "transmit" (uploading data rate) for some Appled devices (in my case, my iPod, but not my wife's Ipad) is what is causing the issue.
Just my two cents.