I don’t think this could happen, obviously. But putting aside even the idea of reversing physical processes, given how our world works, I don’t think it could happen here.
First, I don’t think you could have an observably identical universe after the reverse. The problem is time-lag. I’m not sure it could work given some of the observed processes (distant galaxies) are too far away to look reversed in a day. Astronomers might be confused by what they see (“hey….this star is in the wrong place”; it might make an interesting plot point earlier on in a mystery story with a plot like this).
The second problem is the account presupposes a single moment for everything, i.e., a kind of universal simultaneity, from which processes reverse (or time reverses, so far as the characters can tell). When A dies, everything at that time reverses.
Of course, there is also the question of how to get everything to do that. Except A’s memory. But I take it that’s less of a problem. This is a super-scifi-power, after all.
Finally, I think that, if this involves a universal reversal, this needs a substantial or independently existing time — or at least time which, with respect to the physical world, is substantial or independent. This kind of time, a time not just derived from relations between physical events and physical things — the kind of time discussed by Shoemaker in his paper on time without change (jstor; sorry I can’t find an open access copy), is needed because:
A. The two periods in which change occurs and then gets cancelled out are indistinguishable from each other given only their physical processes; if it’s universal, then the processes which reverse are all the physical processes. What distinguishes the forward and the backward sets of physical processes is only that: – that one is forward (whole egg, smashed egg), the other backward (smashed egg, whole egg).
It looks like we need something physically independent for the temporal order by which one distinguishes forward and reverse.
B. No-one except A remembers it, and A’s physical body doesn’t ‘remember it’ either (being no longer dead). After each new reverse, (excepting A) we have the equivalent of the unobserved and unremembered period of time in which no change occurs. And even with A, given the story, the reverses are unobserved and unremembered. This makes them like frozen regions in Shoemaker’s paper. Whatever happens during that time is traceless afterwards; there might as well have been no change. What happens is the equivalent of a tree falling in the forest when no-one is around, except that, before anyone turns up, the tree gets back up again.
There is one more thing this story needs: that it is possible for psychological or conscious processes, e.g., memory, etc. to survive independent of physical processes. Otherwise, A would have their psychological/conscious processes reversed along with the physical processes. They’d lose their memory as well. They might have the power but it would do them no good. In fact, it might just curse them to an eternal loop — one very similar to the original situation in an episode of Star Trek (‘Cause and Effect’).
In any case, I suppose all that matters is if the characters believe that this physical reversing is what is going on. if they do believe this — or at least A and B believe it — we can make sense of why B would shoot A, or help A at all.