I found the answer to my own question by accident shortly after posting this last year.

The bash script is still technically SSHed onto our main working server, and without manually exiting the script, the connection will go stale and wreak havoc on the Docker container behavior. I do not know WHY the Docker container misbehaves so badly when this connection goes stale. I believe it may be because that script is still trying to run and maintain an SSH connection despite being long disconnected from our main server.

If you are doing any kind of remote connections from your container to another server/environment, make sure you cleanly sever those connections after you perform your tasks. Alternatively check your server's ssh timeout.