On my Android, both K-9 installations periodically hang in the outbox. In some cases the emails will not send at all when they have small PDF attachments of <2mb size.
It happens on 2 different Android phones which are fully updated and using the latest K-9 version.
Welcome 
If a message fails to send, K-9 Mail will generate a notification including the response message from the server. What does this error message say?
Where do I find that in Android?
Normally it should show as notification if sendinfmg fails. But maybe you need to provide debug log from K9 here
I am having the same issue. For me the Alert says:
Failed to send some messages
Application-specific password required. For more information, go to Gmail Help…
I did setup the application specific password in my Google Account for K9 outgoing and when I set the password in the Outgoing settings and clicked Next it seemed to take it but the messages still sit in the Outbox and I get this alert.
I fixed my issue… I recently switched phones and when I copied al the apps and their settings to the new phone the outbox stopped working. I never switched to using oauth 2.0. Once I did that the outbox started working.