DSL Modem and Airport Express Help

I have recently purchased my 1st Mac and love it. The only problem that I am having is with my Airport Express and my Bellsouth DSL modem connection. I have set up my wireless network successfully and Airport sees it. My problem is that my Airport loses it's connection with my network on a regular basis especially after an extended period on inactivity. The only way that I have found to get myself back online is to unplug power to Airport and restart. It then re-connects to my network. This could be 30 minutes or overnight. My DSL modem is plugged into my Airport. Applecare intially helped me get online by advising me to set up Airport to connect using Ethernet and DHCP. BellSouth tech support is of little or no help. They mentioned a PPPOE configuration but really didn't seem to understand Apple or my plight. I guess my question is: I'm not sure if I have my Airport configured properly? Has anyone had any experience with BellSouth DSL service using an Airport Express? Thanks