I had a similar problem with the random signouts from the P$N etwork it was an option set in my router for wireless. Im going to assume the menu's are the same as im running a netgear router myself, but if you go into the wireless setting section you will probably see this
Wireless Access Point
Enable Wireless Access Point
Allow Broadcast of Name (SSID)
Turns out it that by my disabling the SSID the network on the ps3 stopped droping, though by doing so your other wireless connections may die at the same time, but i was able to run most of my wirless connections with the broadcasting, hopefully this may help you.