Will Abe quit trying to get the Box to work?

Question

At the end of Primer, there are two Abes and at least three Aarons. Box-Abe tells not-narrating-Box-Aaron that he's staying to watch over everyone and to sabotage not-Box-Abe's Box so that he and not-Box-Aaron eventually give up. How is this supposed to work? Does Box-Abe not remember violently drugging his other self and locking him up for days? Does he somehow think the other Abe and Aaron won't remember anything of their experiences, and won't find out that other versions of themselves have been doing things in their absence? The obvious conclusion they would come to is that the Box works, and they will use it.

Answer 1

Box-Aaron asks some of these questions himself during the conversation in the airport, and I believe Box-Abe's responses in that conversation are the best answer we're going to get from the movie itself.

Abe: I'm staying here.
Aaron: Why? They'll be building their own boxes in another day. And yours already knows what they've built. You're not going to be able to watch them forever.
Abe: The box Abe is building won't work. He's got it wired wrong.
Aaron: And if they fix that...
Abe: I'll start actually taking pieces out of it. It's just a gimmick. It doesn't work anymore. Your double will say they have to move on to something else. And mine will agree. They're friends.

(I don't have proper access to the movie right now so these dialogue tags are mostly guesswork; I'll fix it when I do find a copy)

Based largely on this dialogue, I would answer your questions as follows:

How is this supposed to work?

Box-Abe will simply keep sabotaging Other Abe/Aaron's boxes as many times as he needs to until they decide to move on to some other project.

Does Box-Abe not remember violently drugging his other self and locking him up for days?

He probably remembers all of that.

Does he somehow think the other Abe and Aaron won't remember anything of their experiences, and won't find out that other versions of themselves have been doing things in their absence? The obvious conclusion they would come to is that the Box works, and they will use it.

The Other Abe/Aaron don't know for certain that they have working time travel boxes yet. They have yet to do any actual time travel themselves. So it seems unlikely they'll jump all the way to "the guy who locked me up must be my past self trying to prevent me interfering with his time travel shenanigans", especially since they never saw who locked them up, and Box-Abe's going to stop them from successfully testing their own human-sized time travel boxes.

Admittedly, if Box-Abe is sloppy with his sabotage and lets Other Abe see him sabotaging the boxes, in clear enough view he can tell Box-Abe is also Abe, then I would expect Other Abe to work out what's really happening. But I'm assuming Box-Abe will not be that sloppy.