There are several possible reasons that messages seem to 'disappear'.

There are two types of email accounts: IMAP and POP. See https://support.mozilla.org/en-US/kb/glossary-terms-including-types-accounts

If you have a POP account and are accessing the mail on more than one computer or smartphone, whichever device reads (downloads) the message first will have it locally, but it will no longer be listed or available on the other devices.

If you have an IMAP account, the message stays on the server, but if one device (user) moves or deletes the message, it will affect the view on all devices. So, for example, if you are using your smartphone and take some action on an email, when you get back to your computer, it will reflect that same action (but you might not have realized what caused it).

Sometimes the index of a mail folder (.msf) will get corrupted. If you right click on the name of the folder and select Properties, a 'Folder Properties' window will open. Select 'Repair Folder'. This may take care of the problem.

Another, less likely, reason for messages not to show up in your inbox is having the preference set to show only unread messages. Then once you read them they seem to disappear.

If you are still having problems, please look at the following items and respond with the information.

   1) If your mail server has a browser interface (web mail access such as mail.google.com), do the messages show up there?
       
   2) Right click on the folder in question and select Properties.
       a) Number of messages?
       b) Size on disk?
       
   3) Left click on the account name; View settings for this account; highlight Server settings;
       What choices are marked under "When I delete a message"?
   
   4) What, if any, antivirus program do you have installed?