One thing we need to understand is that all messages that have been affected by the issue 'before' the 9.1 update will still ALWAYS display the same error when trying to access them even after the 9.1 update has been applied, unless you have those affected emails downloaded into your MacBooks/Laptops, they are irretrievably lost forever.
However, yesterday's 9.1 update has now addressed this issue with newly received emails AFTER the update has been installed, well, it certainly has in our case! All new POP emails received in our devices (iPhone 6's or iPad Airs) after the 9.1 installation, now remains in the Apple Mail app, exactly how it should, even after those emails have been removed from the POP mail servers.
My team of 12 staff, including myself, all use iPhone 6's and iPad Airs now running on iOS 9.1 and, so far, NONE of us are experiencing the same issues with 'messages not downloaded from the server.', like we were before the update was installed.