it all depends on how you set up the way time travel works.
it should actually be just fine, as far as i can tell. you just need to use the "interfering in the timestream causes a parallel universe to come into existance" version of time travel (which, really, is the one that makes the most sense, imo).
now, many authors have a single closed timeline, where cycles can occur. isaac asimov (one of my first favorite writers) wrote one like that called "the end of eternity." i won't go over the whole book, but it dealt with a closed loop (guy goes back in time so he can teach another guy how to create the first time machine...). the thing is that loops like that have no logical entry point. if guy #2 needed guy #1 to come back and teach him how to make a time machine an guy #1 couldn't go back in time without a time machine, then how could it ever have happened?
what you need is a system of parallel universes. guy #1 goes back in time, talks to guy #2. that trip spins off an alternate universe. then, if guy #1 goes forwards in time again, he goes into the future of the second universe, not back to his original universe (unless he has a way to travel between universes).
so, in your case, here's what happens:
person B talks to person A. it doesn't matter that person B hasn't physically travelled back in time. there's been a change made. as a result of that change, person A survives. the trick is that person A's survival is a result of a change in the timestream. that means that we're dealing with another universe.
in universe 1, person A died, and person B called back in time.
in universe 2, person A lived, which means that Person B has no reason to call back in time and also has no memory of having called back in time (because the person B of this universe never made the call).
it can be a little tricky if there's more than one call (technically, the second call should go to Person A of the original universe, not the person A living in the parallel universe which was created by the first call) but it can be dealt with.
you can just gloss over that bit, and i'm sure no one will mind.
you could give person B an equipment upgrade, so that he remains "locked" onto the "correct" person A, even if they are in different universes.
another possibility is to dump the "parallel universe" thing. rather, you have a single self-correcting universe. person B makes the call. the timestream after the point at which person A recieves the call has now been altered. still, person B has made the original call, and may well remember having done so. after all, there's still reason for person B to have made that first call. after subsequent calls, however, person A avoids the brush with death. at that point, person B has no reason to call back in time. the change has been made, and the timeline progresses from there. since there was no reason for person B to have made the call, however, person B will not make the call and will have no memory of having done so. persona A is alive because the person B of the *original timeline* made the call. if it helps, think of it as a parallel universe which ceased to exist once the new one split off.
does any of this make sense to you? does it solve your problem?
Paul, off in a universe of his own...