I can't see that happen, first it would mean that our lifes are dictated by a preset fate that could not be changed, and that the travelling in time was set out for us to do if we did it, and we would have lived our exact same lives an infinite times - and will to the end of time.. - the explanation reviels itself by reading this post..
I don't see time travel this way because it would mean that the dimension of time is bent in a loop like manner, this would indicate that the expanson of the universe would suddently start as the big bang once again with the blink of an eye.
Or the universe would expand then later collaps in the big crunch until reaching the point of a singularity then start the precise same big bang again resetting time, exploding in the same way - and every particle moving in the exact same way and so on (this was what i ment in the intro - with predictated fate). This seems very unlikely next to a new big bang continuing time where it was left, exploding in a new way, particles and atoms flying in random ways and setteling in (most likely) new ways. The universe have always seemed to have acted in a rational/orderly way.. excecpt from singularities where everything stop making sense.. What happens there could actually prove you right!, but then again it could prove everyone's wild ideers right...
The other possibility would be that as you travel forward in time you would first pass points in the future time, and as you travel on you would pass the same points once again, then pass the point where you first started out, then passing points in the past.. This would indicate that the expansion of the universe would end in the big crunch, and that the big crunch would some how reverse the the arrow of time to make eveything act in a reverse way... like first you die, then you get younger and younger until you are born and so on.. but then again you would only be able to go as far back as to the time when you were born (actually to the time when you entered your timemachine,... but then you would have seen the future)... If you then somehow find a way to become static, so that it was not you moving in the in the dimensions of space and time, but they were moving for you to see from your static place at a safe distance, you would be able to watch as time enter "your" past from your point of view... Right now it seems more unlikely than likely, because it somehow seems very disordered in a universe that tries to make order..
Pardon my english... it's not my mother tongue... hope you can understand my view on the matter.