If a statement on a slave produces an error, the slave SQL thread terminates, and the slave writes a message to its error log. You should then connect to the slave manually and determine the cause of the problem. (SHOW SLAVE STATUS is useful for this.) Then fix the problem (for example, you might need to create a non-existent table) and run START SLAVE.

MySQL Enterprise.  For instant notification when a slave thread terminates subscribe to the MySQL Network Monitoring and Advisory Service. For more information see http://www.mysql.com/products/enterprise/advisors.html.