What is appearing in the logs of both servers in regards to the connection failure?
As shown on syslog:
[ERROR] [MY-010584] [Repl] Slave I/O for channel '': error connecting to master 'firstname.lastname@example.org:3306 - retry-time: 60 retries: 1040, Error_code: MY-001129
The last error code given, after a stop slave and some changes to the master (file and log_pos), was Error_code: MY-002061, the rest of the line was the same.
Again, I have no idea what these errors actually are, nor why they went away as soon as I connected manually to the mysql console with the replication user.