It looks like I finally manged to break it.
I went for a walk (during which I inserted a few waypoints, just for testing), then went to the supermarket. When in the supermarket I know it lost the GPS signal, because I checked. When I came out it picked it up again and continued recording though, so no problems to that point. By the time I got home it had been recording for over 24 hours (and by then about 1100 points) with no problems. So I decided to try a couple of other things. I launched GPS Status to see if that would screw anything up. That's not the GPS status screen in Locus, but a separate app. It found the satellites OK, so I exited and checked Locus. Still recording! Next I went into the GPS status screen in Locus. It showed no satellites. Is it supposed to work when recording is on? Then I hit the three +'s at the top right, one after the other, each time backing out of the settings and back to Locus. Still "No Satellites", so I backed out of that screen. Now Locus is not recording! The status still shows recording (my notification bar shows recording, and the recording icon is gray, not black), but if I move around Locus doesn't do anything. It doesn't even know I have moved! I have left it in this hung state for now, in case you read this and want me to try something. If you do, just let me know what to do.