Of course, I had had this problem for days--even after a complete system reboot--but as soon as I asked the question, I figured out the solution.
My 3rd level basement is offset to my upper two; almost none of it overlaps. When I was trying to place stuff in it, I was actually in the View level for the second or even first basement level. But when I happened to click down on the View, to where I'm actually in the 3rd basement, everything reappeared.
That's probably due to a rendering setting that reduces the number of objects shown in the distance; people with higher resolutions might not have the same problem. But I'll leave my question and solution up, in case anyone else runs into the same problem.
Solution: Make sure you're viewing the floor you're actually working on!