There was an option in the old K9 client to tell what should happen to emails on the server after downloading. I can’t find such setting in the new version.
If I set “When I delete a message” to “Delete from server”, and delete the email locally, then the concerned email remains on the server, and gets downloaded again at the next poll. In the other case, when I set it to “Do not delete on server”, then it remains on the server too, but won’t be downloaded again at the next poll. Totally confusing. It seems like K9 would like to simulate as the message would be deleted on the server, without actually deleting it remotely. (It is just the icing on the cake, that the “When I delete a message” option behaves the reverse way.)
All this stuff worked correctly in the previous public version, so I don’t think it would be a prococol (pop3) limitation.