Primer is by far the most sophisticated time travel movie I've ever seen. Did you know that director Shane Carrurh wanted the objects to stay inside the box when traveling back in time, so they keep their relative position in space? (remember that earth is moving so they need to challenge space as well as time, in order not to appear somewhere in outer space). In other words, they stay inside the box the whole "times", no matter "when" they pop out of it. The box keeps it's location on earth, and so are they. He mentioned Back To The Future where the DeLorean couldn't have possibly knew the location of which it needs to pop out at (?! sorry for my bad English, I hope this BTTF plot hole is understood). Carruth made a lot of efforts to untie any possible paradox.
As many others, I've watched the movie quite a few times and read a lot of information about it. The following suggestion refers to the most common analysis of Primer's timeline, and can be seen here.
It is assumed that Aaron and Abe visit the party many times before making the successful move (where the gunman is arrested and Rachel is safe). But when you think about the mechanics, there seems to be a paradox:
In order to go back after a failed attempt (or just an observation) they must have a box running. But when they go back in time, in the new timeline their doubles are also going to the party to have their attempt. Suppose the originals convince the doubles not to go, and let the originals go instead, since they have more experience. If they fail again this time, why would the doubles agree to stay in this timeline, where the party goes wrong? This implies both the originals and the doubles must go back together, which makes sum of series of doubles. Even if they stay in the hotel when the party is going, letting the ones that come out of the box to go there, there are still 2 sets of each person stuck there if they fail.
I can't think of any conventional way they could have loop over the party more then only one time. In this theory, they got it right the second time, and sent back the doubles with explicit orders of what to do. The originals would then stay in this timeline, and these are the ones we see arguing at the airport. It is possible that the doubles would fail and get stuck with the new doubles as explained above. In this scenario they will not get to the same airport scene.
If I squeeze the juice out of this theory, and add that 1) Aaron mentioned the term "sum of series" at the beginning of the film, and 2) considering the mindf**k scene at the end where he builds a huge machine, this could support the theory that they failed multiple times and are trying to fix it. Although this is a very flimsy theory.
Could anyone come up with a way they could loop back more than once?
I am again sorry for unclear language, please feel free to ask for clarifications.