Ssh – disable no-more-sessions@openssh.com on ssh

UPDATE: For an actual answer see zero_r's answer below

This isn't an answer, but a workaround. Use screen.

When you first log in, run screen. You get another shell, run commands in that. If you're disconnected, the screen process keeps the terminal alive so that your shell and the processes it is running don't fall over. When you reconnect, run 'screen -r' to resume.

There's a bunch more to configuring and using screen, but the above should workaround your problem.

The first thing to do in this situation is to use the -v option to ssh, so you can see what types of authentication is tried and what the result is. Does that help enlighten the situation?

In your update to your question, you mention "on another local Ubuntu". Have you copied over the ssh private key to the other machine?