Could it be that pg_basebackup is still running and your CONNECTION LIMIT on the replication user is preventing any more connections?
They are literally back to back. I didn't log the disconnections at first, but when I turn that on you can see they disconnect back to back also. pg_basebackup finishes quickly. I can see its progrss from the standby server.
I removed the connection limit completely on the REP_USER, and also started trying to use the superuser for replications. It didn't make any difference alas.