I just remapped all the planes, and I think I discovered the problem: a bug in o2.
Turns out that the images remain visible ONLY AS LONG AS THE FILE IS OPEN, and, moreover [here's the confusing part], ONLY AS LONG AS THAT VIEW [FRONT, SIDE, TOP] IS VISIBLE.
If I change my window views so that the FRONT view fills my work area, then change back to the standard 4-view layout [using F9 or the Windows|Standard (MAX Layout) menu item], the image won't display, and nothing I've tried will make it display except to totally redo the mapping again.
Reopening the file later also fails to display the images, so I have to leave the file open or redo the mapping every time.
Since it's impossible to tell how far I can drag a window's corner before it squeezes out the other windows, I pretty much can't risk filling the work area with just one window anymore. Oh well--at least now I know:
Thanks for your suggestion--at least now I know:
1. I can't drastically alter the window layout while using these planes as a tracing guide;
2. I can't close the file until I'm done tracing [or, in this case, done with Klink's tute];
3. You guys are great. Thanks for the help!