I think what you are saying is that you would like to delete mail on your iPhone but have the mail stay on the AOL server. That's not a problem if you use POP3 as your setting in iPhone. If you use IMAP then whatever you delete on your phone will be deleted on the server. What option do you have now?
Hmmm. Perhaps AOL defaults to an IMAP setting. I don't use AOL so I don't know for sure. What I would do is I would add a new mail account and not use the "AOL" choice. I would use the "Other" choice try this:
3. Add Account
5. At the top it will say "IMAP", "POP", "Exchange". Select "POP"
6. Fill in the other fields:
Name: "your name"
Address: "your email address"
OK. Last thing to do. Call AOL and ask if they support POP3. If they say yes, then ask them what the server name is. "POP3.AOL.COM" may not be the right server name, or they might not support POP3. If they do support POP3, then we just have one of the parameters set wrong...