Oh heck! AOL seems to be a law unto itself, doing things differently to every other internet company!
It might well be a syncing problem between your iPad and their server though. So (assuming that you've actually got an email address that includes 'aol' in it), I suggest getting to your email
directly (via AOL's website), rather than hoping to find it through your email app.
So, DON'T open your email app. Instead, open your web browser. (If you're viewing this thread on your iPad then, clearly, your web browser is already open). Then go to this website:
https://mail.aol.co.uk
You might see a message asking you to confirm that you're happy to continue using Oath's services. (Oath is the company behind AOL and Yahoo). If so, click the button to accept.
You should then be able to log into AOL's webmail service. Once you've done so, you should have access to all the mail that's held on AOL's server. Hopefully you'll find the email you're looking for there.