Just a few more thoughts on this.
Is it possible that your PS3 is connecting to your Linksys rather than your Belkin? Is there some config screen on the PS3 that you can check, maybe compare gateway IPs or something?
One way to test I guess would be to turn off the Belkin while using the PS3 online and see what happens. If the link drops you were connected...
Alternatively, is there a way to connect the PS3 to the repeater by cable? Having the connection like this: modem -> cable to wireless (Linksys) -> wireless to repeater (Belkin) -> wireless to PS3 is just a recipe for trouble.
I can't see the need for a repeater if the base station is only 10m away.