MySQL replication can break for a wide multitude of reasons. The
following is a quick and dirty way to resume replication, if the error
that appears in the output of SHOW SLAVE STATUS\G indicates that
replication stopped at a specific record.
It is a dirty way, because immediately after using it the database on the slave becomes different from that on the master by one record. If you can live with that, the skip-one method can help you quickly put the slave back in track.
On the MySQL CLI:
mysql> STOP SLAVE;
mysql> SET GLOBAL SQL_SLAVE_SKIP_COUNTER = 1;
mysql> START SLAVE;
mysql> SHOW SLAVE STATUS\G
Hopefully your replication will resume after this, and the value of
your Seconds_Behind_Master will quickly be depleted.