I saved several .psd files to my computer. They appeared to save successfully - the progress bar went to 100%, and I closed the app. When I re-opened Photoshop later and selected the files from my recent projects panel, I got the error "Could not complete your request because the file was not found. I couldn't locate the files anywhere on my computer, and I ended up losing hours of work.
This is the second time I've had the issue. Is there a way to prevent this error?
Not what you want to hear, but don't rely on the recent files list. Use a proper file browser, and organize a sensible folder structure so that all files have a logical path. That way you can always find them.
Files don't disappear. They get mislaid, saved where you didn't intend to save them.
The recent files list is intended as a convenient way to pick up where you left off after a lunch break. It does not keep track of your files. It's just static and dead pointers to a location on disk, even if the file is in fact elswhere.