Time Machine never finds anything

10.6.8 Mac Pro backing up with Time Machine to an external USB drive. No errors reported. When I enter the TM and search for a particular file name from a couple of months ago (in a backup set that does exist), the bottom of the Finder window says "Searching" and the little gray dashed circle keeps going around and around but that's it - it never finds anything, no matter what I search for. What's going on - why doesn't my TM work? It's not very useful if I can't ever search it for anything.