Sometimes critical jobs might terminated because they faced a deadlock situation and was choosen as the deadlock victim by SQL Server. The other process which was allowed to continue
may be a stored procedure call from a web page, and a failure on that would have impacted a single user's session. But the failed job might impact all users of the application.
In these scenarios it is ideal to run the critical jobs with a higher deadlock priority so that they are not chosen as deadlock victims.
We can set this connection property to appropriate level and SQL Server will terminate one with lowest priority. This feature is available from SQL Server 2005 onwards.
By setting the deadlock priority to high we can prevent our script being terminated as deadlock victim as shown below.
SET DEADLOCK_PRIORITY HIGH
SET DEADLOCK PRIORITY NORMAL
You can give a numeric priority from -10 to 10 as well incase you want to set different priorities for a set of scripts which are expected to execute simultaneously
with a chance of deadlock.
Please refer to http://technet.microsoft.com/en-us/library/ms186736.aspx for more details.