Hello Everybody:
I used to have the same issues.
I have and Airport Extreme conected wiresly to and Airport Express, that I use ONLY for Airplay (join network).
This can sound a bit ironic, but the problems began when I change the chanel of the airport extreme, that was one of the solutions mentioned here. I did that because I wasn't recieving the Internet Speed in the second floor, and for that work excelent, but the AExpress began to drop every 10 to 12 hours daily. I Did a hard reset, downgrade the firmware an so on and nothings happend.
This solution only applies to the people who have:
AIRPORT EXTREME AS A MAIN ROUTER
AIRPORT EXPRESS AS AN AIRPLAY SPEAKER
I change in the Airport Express the protocol... instead of DHCP, I change it to "Static"
If you use the Airport Express only as a speaker, you dont need internet on it, you just need that device in your network, so if the DNS message apperar, just ignore it, and go ahead... we need the Airport Express just as a speaker, not to extend the network.
NOW, I have a Bose SoundDock10, that doesnt requiere internet connection (Internet radio and so on), so, if you have a system that WILL require internet, this solution is not for you. The mention above have worked out for me for about a month ago flawlessly
I repeat: If you use your Airport Express to extend your network, maybe this will not be a solution.
BUT if you use it as an AirPlay Speaker, I'm pretty sure this will work it out.
LUCK