I wouldn't rush to buy Linksys again, the Ethernet to wifi bridge works with very few things that I have plugged into it and now the AP has proved it isn't up to the job.
Try using DD-WRT firmware on the AP, it'll probably make it more stable, I've always had issues with the stock firmwares.
From memory, the version of the WAP54G that I have isn't supported by those third party kernels.
Edit:
Looks like it is now:
"WARNING - DD-WRT was not originally intended to be loaded on a WAP unit. It was found that it will run but it is a tricky unit to load and have function correctly. Below are a compilation of methods/instructions to assist you with creating a DD-WRT loaded WAP unit."
http://www.dd-wrt.com/wiki/index.php/Installation#Linksys_WAP54GI have no desire to start messing around with that for just an access point.