Here recently every time I try to log onto the network it fails or logs on then kicks me out! I am about to sell my playstation an just keep our Xbox!
Its highly unlikely its your ps3 thats causing you problems, and more likely your network / ISP/ or router. Also, if your NAT type 3 then that definitly doesnt help. I used to have NAT type 3 and had all sorts of problems with logging out and connecting with online games.
If I were you I would call your ISP, and troubleshoot. If that doesnt help then you can troubleshoot with a sony tech by calling 1-800-345-7669.