It sounds like your mail files get corrupted.

Try to rebuild the index file of the troubled folder. Right-click the folder - Properties - Repair Folder

Note: depending on the corruption this may erase messages from the affected folder which cannot be recovered anymore. In that case you'd need to restore them from a recent backup. http://kb.mozillazine.org/Thunderbird_:_FAQs_:_Backing_Up_and_Restoring

Corruption is often caused by anti-virus software messing with Thunderbird mail files. It is therefore recommended to create an exception for the Thunderbird profile folder, so that the real-time scanner won't attempt to scan the profile with your mail.

For more information on the profile location see http://kb.mozillazine.org/Profile_folder_-_Thunderbird

Thank you for your suggestions. Maybe I didn't explain enough what i did already--or exactly what was happening. I already had disabled the anti-virus software (which I didn't mention). And I already DID right-click on properties to repair the folders. And then all the emails were there. This was true with each folder I went to--IN, SENT, DRAFTS, TRASH, etc., and with each different address with each different server I was using. But the minute I went to a different folder, then came back to the one I had just fixed--the emails were gone again. When I repeated the repair process, they all re-appeared. Even when none of the messages are visible, I can still see in the left column the number of messages I should have in each folder, and I can see WHEN a new message appears--even though I cant see the message until I repeat the repair process to that particular folder. I also have re-installed TB, but did not delete all the files associated with it--and that didn't help. Now I can't even find my Profile folder--and not even the library folder associated with my username. I get a message saying my library folder is invisible. It sounds like a comedy of errors, because the answer probably lies somewhere in my system--and I did forget to say I am using a Mac. I think it is something I don't need to bother you guys with, and will just continue to work on it on my own.

I suggest trying to rebuild the folders according to the instructions here. Essentially, you copy the messages to another folder, which in your case may work after a "repair", then delete the underlying mbox and msf files.

It may not be possible to recover your existing messages, but with new folders in place, you shouldn't have a recurring problem.

Thank you both, sfhowes and christ1, for your suggestions. In the end I do want to go back and work more with TB, because I believe with these suggestions I should be able to get it to work. Meanwhile, I got tired of working with it, and found a new email client, Airmail, developed especially for the latest Mac OS, El Capitan, which I recently installed. As soon as I installed AirMail, all the folders and all the emails were immediately repopulated, in probably less than a minute. So I think I will stick with it. Although it bugs me I haven't as yet solved the problem with TB, as I have used it for years, so eventually I will go back and use your suggestions to try to make it work. Thank you again. So I am marking this "solved"--even if it was outside the box. Thank you again.