Go into the router and use the security features to block the ps3 when you don't want it online. Wifikill does not actually kill the WiFi it is a stupid ARP spoofer. It also tends to degrade the performance of the device you do it from since all traffic now comes to it. Many routers have wireless isolation to prevent exactly this attack.
Likely the reason you are getting kicked off is strictly because he has a better signal level to the router than you do and he is using so much bandwidth your device gives up due to errors and resets the wireless connection.
There is one way to actually kick someone off a wireless AP but I will leave it for you to research it requires the use of UNIX and wireless device you can set to...