How to figure out what type of account you have in Aquamail:
In the account list view, long-press on the account in question, choose "Options and Folders".
The second to the last menu option will say "IMAP options" or "POP options".
1. Check what you see in the webmail interface, by going to
http://webmail.cox.net/Do you see those messages that you are not seeing in Aquamail?
2. If you don't see them, - it is most likely that either Outlook lost (or never had) the configuration "Keep mail on server after downloading", or there was some other glitch.
There is not much you can do to get those messages in Aquamail if they are absent on the server.
3. If the messages are still visible in Webmail, instead of configuring the number of messages to sync, try changing that to a number of days (30 days). (The number of messages to cache, - set it, say, to 200.)
In any case, I wouldn't set such huge numbers to sync/cache. The huge numbers can give you all sort of problems: your connection can time out before you sync all messages, you might run out of space on your phone, or the database on the phone will become so large that it will cripple down both Aquamail and the entire phone.
In general, POP3 is a bad choice when you are accessing your e-mail from multiple devices/mail clients.
While you can configure certain options to make it working with POP3, I'd strongly recommend switching both e-mail programs to IMAP.
See Cox's help page for that:
http://www.cox.com/residential/support/internet/article.cox?articleId=a8fb24c0-6440-11df-ccef-000000000000#switchingfrompoptoimap