First, how are you connecting with the PS3, is it cabled directly to your modem or, are you connecting via a router? If you use a router, try connecting via a cable directly to your modem. I know that seems odd but, PS3 and some routers have issues and, will only work together intermittently. If that works, and you've bee using WiFi but need to go through the router, try cabling to the router at least..
My granddaughter had the same trouble with her PS4, finally had to play trial and error with routers. Turns out a Cisco (Lynksys E2500 Model) is the only one we cold find locally that worked consistently for one solid week. She's had it for 3 years now, and her PS4 still connects to every server, every time (unless the servers are down and, there is a notice form the game developer stating such.)
