i don't know anything about qtopia, but the problem is, i believe, a result of AOL (and Netscape, too, for their Webmail service) using a non-standard bastardisation of the IMAP mail protocol. there are, as far as i know, no open-source clients capable of using this totally non-standard protocol.
however, if you really do need to access your AOL mail from a linux box, you should be OK with the Netscape Navigator mail client. it certainly works with Netscape webmail.
Netscape isn't open-source, and it differs in its support for said mail protocol from its open-source sibling Mozilla (which does NOT support Netscape / AOL mail).
This was the only solution i had to adopt for my father, and involved a 16MB download from Netscape's website (annoying at 56k dialup!!) - the browser is available for x86 Linux distros.
hope this helps (even if it wasn't quite the news you were probably wanting!)