Well, I don't think I'm really doing any resource allocation. Most of the Tile Editor is written in VB6, which handles memory management more cleanly. And the Alt-Tab functionality is built into DirectX (I didn't do anything to support it). And I suspect that since this doesn't happen everywhere that it is indeed driver-dependent. But maybe it's just that nobody has used Alt-Tab frequently enough to see the problem.
Anyway, one more thing to check if you create your graphics externally. Make sure the tileset bitmap is no wider than the display for your game. The map editor can show you the tileset and scroll vertically if it's too big to see all of it, but it won't scroll horizontally.