When I import a folder I get the usual series of previews/thumbnails, but after the files are imported all of those small previews vanish. When I open them in Develop mode I am able to see them and work on them but again, the small preview sticks around for three of four images and then goes blank. When I export the finished images they are seemingly fine and function normally, for example in Photo Mechanic. I am mystified.
Sounds like you may have a corrupted previews cache. Quit Lightroom. Open your Lightroom catalog folder, and remove the 'catalogname previews.lrdata'. Trash it or place it somewhere else for the time being. Then start Lightroom again. Lightroom will rebuild your previews cache, so initially you won't see any previews, but then they should appear one by one.
It worked! Thank you.