I actually got motivated and worked on it today.
Hasn't worked out so far. I looked carefully under the 40X LED magnifier, thought I saw one connection point that looked a little lifted. I tried tap re-soldering each of the four connections, and even the two on the sides, didn't help. Now I've removed the entire USB plug, and will have to try microsoldering the four wires from a USB cable on to the contact points, but the contact points don't look so good now that I removed the plug, so it may be a lost cause, at least for someone who doesn't really know what he is doing.
This USB stick was backed up about two weeks ago, so all I am losing is two weeks of work, so it's more of a project than a dire need, but I haven't given up yet.
It is teaching me not to rely on these sticks and keep them backed up though.