The SPS Alert service schedules and sends email notification alerts to users when documents, lists, or list items are created, updated, or deleted. If this service is stopped, users will not receive alert notifications.
A service can stop for many reasons, including:
The service was stopped by an Administrator.
The service encountered an exception that stopped the service.
The service was improperly configured, which prevented it from starting.
The service was prevented from starting because the user account assigned to the service could not be authenticated.
The service can be restarted using the Start SPS Alert Service task:
Start Alert Notification Service
If service is unable to restart successfully please refer to the tasks output which will indicate the cause for the start failure. With this information, the Services snap-in from the Computer Management console can be used to take additional resolution steps:
Start Computer Management Console