SQL Server 2012 Express dying randomly
ERROR 17300 is caused by SQL Server not being able to execute one of the system tasks.
It points to insufficient memory: http://technet.microsoft.com/en-us/library/cc280564.aspx

As that resource explains, it could also be caused by a setting, but insufficient memory is more likely the cause.

ERROR 17312 is directly related.

This could be caused by another process eating up all the available memory. For example Windows explorer file copy operations are known to reserve memory and not release it.

Make sure you have adequate memory installed on the system and monitor how much of it is reserved.