Does my samsung tv keeping turning itself off because of not having plugged it into a surge protector or is it more a fault with my tv

Surge protector's do not switch off any device, unless the surge protector is faulty itself. If the TV wasn't conected via a surge protector and a surge did come down the mains (often during thunderstorms) then it could cause a fault.
By the way a protector only stops a surge once, after that the protector should be scrapped. It's best to buy the one's with the light that lets you know the surge circuit is working, therefore.
So your set is faulty. Unless you have set some kind of timer on it by error.

It is a fault with your power supply module actually inside the tv...take it to a local service center or if its under warranty take it back. surge protectors help prevent issues like this occuring due to damage to the power supply from surges but not having one wont cause these problems unless it has recieved a surge.....in future i would use a surge protector on all your expensive appliances, surges and power fluctuations are very common in mains power i live near the mines and we have power problems all the time!! hope this helps,ben