This sounds like it could be one of two things. Either some DHCP hiccup like the previous posters have mentioned, or maybe a wifi interference problem. Is the PS3 hooked up via wifi?
I had a cheap router once that would try to assign the same IP I was using to my room mate's computer when he would wake his computer from sleep. This of course caused problems for our internet connectivity even though Airport showed that we both were connected to the router.
Another issue that I've had displaying these same symptoms (with the same crappy router) was that there were several other wifi routers in range (from other apartments) This caused interference with our router, and even though Airport would report that it was connected to the router with full signal, a very miniscule amount of data would be transferred.
A quick solution to both of these problems was simply to turn airport off and back on again. Obviously for the first problem it would get a new DHCP lease, and I can't say why it worked for the second problem but it did.
Hope that helps.