Hello, Welcome to discussions.
AOL on iPhone should be setup as an IMAP account. It seems like your account on the iPhone is acting like a POP account.
You want to ensure when you add an AOL account to Iphone you go to
-Settings - Mail,Contacts,Calendars- Add account - AOL Mail - Type in your info. And save. This will save the account as an IMAP account.
You may also wish to check your iPhone Software version and update if it has not been updated in awhile as there has been some mail improvements.
You can check your version by connecting to iTunes on the Summary screen or via Settings-General-about.
http://www.apple.com/iphone/softwareupdate/