The problem seems to be that the server doesn’t support the IDLE extension, so Push doesn’t work. Unfortunately, the code is not doing the right thing in that case and K-9 Mail ends up sending a command to the server over and over again.
You can get rid of the problem by manually disabling Push for that account. See How to configure Push?
K-9 Mail 5.802 will automatically disable Push for an account when it detects that the server doesn’t support Push.