Time loop?

[dyitto]

Backwards time traveling would be impossible, because of the paradox that a time traveler would change the circumstances that originally led to his/her own birth and time travel trip.

Now how about the idea that a time loop could exist, where the circumstances in the present, past and future of the time traveler just happen to fit?
Using this idea, one wouldn't introduce a time machine in a story, but a person that just did the time-travel-trip - simply because it was his/her fate to do so.

I've no idea if this idea already occurs somewhere but I'm curious.

[Expendable]

Do you mean as in The Time Traveler's Wife? Biggles? The Final Countdown?

Your best bet is for two people who have some kind of bond but exist in different times. Either each one can somehow leap independently or they can somehow pull the other to them, usually when they have a great need. If they pull each other across to their time, how long can those persons remain before they get yanked back to their own time (if at all)?