If you often move a lot of messages between folders, then the order of messages on the server can become messed up -- and this can prevent Aqua from properly seeing the newest ones.
If it's an IMAP account, please try this:
- Long press the account
- Options and folders -> account options
- Change "Messages to sync" from a number-based value (like "25" or "50") to a date range based value (like "Last 10 days").
Back out and refresh the account / folder.
Oh, and please confirm that newer messages do exist in web mail, specifically (as opposed to in your desktop mail app, if you use one).