I have a backwards compatible 80 gig ps3, have had it for years.
about 2 years ago it started turning off/overheating while on ps3 games because graphics were too intense, but for no reason it fixed itself one day without me updating it, and i was able to play ps1 and ps2 games without hassle.
now it turns off while playing ps1 and ps2 games, i played crash bandicoot ps2 game, and shut off after about 15 mins of play, and now i just downloaded the first crash, and it froze after 15 mins of game time.
but it does not freeze on ps3 games and netflix, and i just before it turned o]ff on crash, it was on netflix for 5+hours
it shut off during game play of old games before i updated it
It's tough to say what is exactly wrong, it could just be that your PS3 is pretty old now & is nearing the end of it's lifespan, you don't say if you've done any work on it like replacing the thermal paste etc, that's something that may help, it does sound as though it's possibly over-heating though.
If you haven't already I'd definitely make a back-up of your saved data though.
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First off, sorry for posting in wrong section, did not realize that. xD\
The only work that has been done on it is the blu ray lens. I replaced the blu ray lens, but other than that, nothing really except for a few cleaning maintenance's, like taking off the outer chassis and using the dust off, but i have not done that for a few months.