Are they *old* (not very recent) unread messages?
The app syncs (keeps fresh) a limited number of recent messages, per folder.
Even if you use "unread first", it will not "hunt for" older unread messages on the server. It's just a sort option for the same, recent, messages.
Please try this:
- Long press the account
- Options and folders
- Account options
- Change the "messages to sync" setting to make it larger.
Please don't go crazy with the thousands, since the default is 25-50 (depending on Android version), I'd think 100 or 250 should be enough.