Binary log positions are incremental within each log file. The position resets whenever there is a new binary log. New binary logs are created each time mysql restarts or if the binary log grows larger than 1GB.
Replication should automatically reconnect when you restart MySQL. Check your my.cnf config file for this: skip_slave_start = 1 and remove it if present.
You can run on the replica CHANGE MASTER TO ... MASTER_CONNECT_RETRY=20 to make the replica attempt reconnections every 20s instead of 60s (the default)