Because once the Terminator disappears into the past, the result is known in the future. Kyle isn't 5 minutes behind him, for all intents and purposes, he's 40 years late.
If I go from 2009 to 2006 and kill you, you'll have a tough time coming from 2009 to try and stop me, having died in 2006.
That's the only way ANY of it works. Essentially, the T-800 has to fail before you can try to stop it. And in that case, stopping its primary mission can't be yours, because you already know it failed.
That's what is talked about in the T2 discussion, for example. Arnold isn't sent back to save John, no matter what he says. John sent him from the future, so we know John survives. It's more likely that he's sent back to save Sarah, who probably died protecting John the last time through the loop. When the t-1000 goes back, and John doesn't disappear, he knows the T-1000 didn't kill him (and remembers the circumstances of the attack). Logically, Arnold has to be there to do something else, the most likely of which is to protect Sarah...