Now, if this was a Doctor Who story you'd have big problems with a time paradox like that - the Reapers would start to appear to destroy it.
In a DW / Terminator crossover why isn't that happening? The answer has to be that Sarah Connor and John Connor are still making changes - "no fate but what we make" - and until there's a definite outcome the time change hasn't gelled.
So the whole thing will continue in flux until the humans win (fat chance) or John Connor is killed. At which point the Reapers start to appear, destroying all evidence of the paradox and blotting it out from history. With John Connor gone he can't send people back to the past, which means that he will never be born, which means that there is no reason to ever send a terminator back to kill Sarah, which means that there is no real foundation for Skynet's existence... The whole time loop vanishes forever. Back in nineteen-eighty-whatever Sarah has a boring evening at home, comes back to find that her flatmate and her boyfriend have left a horrible mess, has a huge row with them, and generally goes about her normal life. There is no John Connor, no terminators, nothing. It's all gone, edited out of time by the Reapers.
I pass this along for anyone who wants to use it.