I have a 40GB playstation 3 and was playing with no crashes or freezes for 4 days, it was not until i tried the online version that my problems occured.
It was then constantly crashing in one player mode.
I turned off the screen saver and auto messages (when it tells you a friend is online/offline) and also logged out of the PS3 Network and it has been working fine since.
I also deleted the game save data before I tried the above, but it was still crashing, so I would not try doing this, until you see if the above works first, pointless getting rid of your saved game for nothing.
Hope ths helps!!!!!!!!
I tried with router turned off several times and still had the problems,
However, after looking at other peoples responses over various sites, I tried some of their answers and it works fine,
My Router is currently on and GTA is still working, I am not logged in though!