You should be using DCHP on your router. Setup your wireless signal properly (hide the SSID, encrypt the network with WPA, etc). After you have that setup go to your PS3 and setup the wireless network manually. I know that isn't a manual, but it is pretty straight forward. If you've already setup a network properly, then you should have no issues connecting your PS3 - i was able to do it within 2 minutes.
Step by step:
1. log into your router through a wired connection
2. setup the router to use DHCP
3. setup the network with a strong name
4. hid the network name (SSID)
5. encrypt that signal with WPA or WPA2 if available
6. write down the security key
7. log into your PS3
8. setup a network manually
9. enter all the information you've created from the steps above, including checking the box that says connect to SSID even if not broadcasted
10. bam you should be connected
The only reason you would get kicked off the network is if you aren't using DHCP on the router and the router is actually giving specific IP addresses to the devices. Then if you have two devices that have the same IP you'll get an IP conflict and one device will get kicked off.
The other issue is latency. You can't download or transfer files on your network and expect a game to work over the network. I play Call of Duty all the time, but if i'm downloading something on another computer or transfering files on the same network i will get kicked out of the game.
