Can't permanently delete emails. They delete initially and then reappear minutes later. Help

[AC Question]

I delete them from my inbox and then again from the recycle bin but they still reappear.

 

[Rukbat]

Which email app and is your email (on the server, as seen in a web browser) set as POP3 or IMAP? (GMail was known to do that in IMAP on a gmail account, which is why I haven't used it in a long time.)