Original "Terminator" plot hole?

In the original "Terminator" film, Reese is sent back in time to protect Sarah Connor. They fall in love and he becomes the father of the future leader of the Resistance, John Connor. But, at the end of the movie, Reese is killed. The plot hole is, how could Reese have been sent back to the past from 2000whatever to 1984 when he is killed in 1984 at the end of the film? He should not have ever known John Conner and thus he couldn't have sent him back because he is killed before John is even born. Am I missing something?