I’ve seen similar posts about this 1,2 years ago, but never really a resolution. Certain messages just won’t download.
They will give the “The message wasn’t downloaded because you’re not connected to the server” and there is a “Download message” that I can click. If I click that it says “The message will be downloaded the next time you go online”. Clicking Refresh never resolves the issue. It will download potentially new emails, but it won’t fully load these ones.
If I go to Menu -> File -> Work Offline and then again (to go back Online essentially) it will finally download them.
When this happens, it generally is within emails that are moved via Rules to another folder. I don’t recall it happening to emails in my main Inbox.