Again, the 'recent' command should not be needed to get mail on the PC already seen on the phone. Something is wrong there. It could even be the problem.
In K9 go to server settings and make sure sync deletes and sync read are both checked.
DO NOT use any task killer or memory optimizer. Android is excellent at handling processes and memory with no help from 3rd-party apps or user assistance. Just let Android do it's job, relax and enjoy your phone.
...for a full explanation.