All I can suggest is setting up port forwarding. As I have no experience with Belkin routers I cannot help you with how to do that.
In general, for console gaming port forwarding can add some stability, plus it is what is recommended for GT5P.
Outside of that the only other thing I can suggest trying is disabling UPnP on the router. Those two things are what fixes the issue on the Linksys.
Your problem sounds similar to the Linksys issue where the router resets the connection when the PS3 tries doing something. Disabling UPnP and setting up port forwarding stops it.
The best I can suggest is running a Google search for PS3 and whatever your Belkin model number is to see if others are having similar problems. There could be a fix floating around out there.
As others have stated though, something could be interfering with the Ps3's connection.
Is it in an entertainment center with tons of other electronics and wires? I'm shooting in the dark on this, but I figure it is a possibility.