A WAP54G operating in "AP" mode will relay traffic from wireless clients to the connected Ethernet LAN. A WAP54G operating in "AP client" mode is effectively behaving just like any other individuall wireless client. You would use this mode to connect one device, like a game system or video server, to your wireless network. A WAP54G operating in "Wireless Bridge" mode relays traffic from the Ethernet LAN to another WAP54G operating in "AP" mode (the root bridge). You should use this mode to connect entire wired networks to each other over wireless.
Your configuration seems to call for the latter: You have created a point-to-multipoint bridged network that supports any number of wired devices at each remote location. Occasional packet loss (like pings that time out) is not uncommon over wireless; wireless is not a reliable medium. But it sounds like you may be seeing your bridge links drop every so often. I'd try to determine if all bridge links go down simultaneously. If so, the problem would seem to lie at your root bridge (the "AP" mode WAP54G). If links drop independently, then I'd look for a pattern or instigating event common across all non-root bridges ("Wireless Bridge" mode WAP54Gs). For example, look at WAP54G logs and run a WLAN analyzer near the root bridge so that you can see management and control traffic sent around the time that a link is lost. If you think your root bridge may be damaged, you could try swapping it with one of your non-root bridges to see if that helps.