Are you using the AOL desktop or webmail interface?
It sounds like your emails are being marked for deletion.
Do they delete if you logout and log back into your AOL account.
I suspect you have the desktop software and it acts different than the webmail software.
Do you have a purge option or other second step button that expunges them after they have been marked for deletion?
Look around the available options for the words purge, expunge, or other synonyms for those words.