>> There is about two feet of soil at the base of the fence and then the rock wall is almost vertical for another two feet.
I agree that it's hard to tell from these photos exactly what the base looks like right behind the fence on the sloping side, and that the angle of the wall is key, and that professional advice would be a Good Thing, if advice can be had much less expensively than having them do it.
>> many of the rocks at the base had fallen off of the slope
If they were "just sitting on top of the soil", no problem, they were not holding up the slope. At most they were preventing erosion, which might also be done with tough-rooted perennials (juniper bushes sound great for that: once I had to dig juniper roots out of clay and rocks!)
If the rocks that fell out left holes behind, with other rocks above those holes, then they WERE supporting something and prompt action sounds necessary (but it IS hard to tell). Just pushing them back into place doesn't sound like much, but if you can hammer them in firmly, that MIGHT be all you need. (But more photos might help, and an expert ON SITE who will inspect it for free or in return for dinner or a pie would give 100 times better advice than I can.)
My only useful idea is like what Greene said: build an [u]angle[/b] into the wall to help you. If it really was vertical and not mortared together, it might not have been supporting anything much, just slowing erosion.
If you can carry a few more stones up to the wall, and put it back together at an ANGLE at the base, using up some of the two level feet you have to play with, THEN it should be able to resist subsidence better than before. Like the pyramids: they lasted longer with sloping walls than they would have with vertical walls.
For example, position your biggest stones 12-18" closer to the fence than they were. Backfill the part where the rocks were so as to form an angle. Build the new and big rocks into the angle, and merge that with the existing wall.
I assumed that backfill should be the heaviest clay I can find for a concrete-like base, but maybe "well-draining is better.
