Where are they stored?
Open the Options dialog | Advanced | File Locations section. Please see the Projects, Maps and Templates folder location.
Now quit Offline Explorer Pro, open Windows Explorer and browse to that folder. Select all files with the webdown filename (webdown.dat is the Projects file, the rest are backup copies) and copy them to another directory to keep them intact.
Select the most recent file with the maximum size and copy it back under the webdown.dat filename.
Start Offline Explorer Pro to see if all of your Projects are in place. If something is wrong with the Projects list, try to repeat the process with another webdown file.
I followed your instructions above and the webdown.dat file is only 1kb.