A Before or After Action added to a backup set for the purpose of starting or stopping a service or process does not do so. This happens each time the backup set is run.
When Before or After Actions fail to change the status of a service or process, it is usually because the start or stop request is not executed with sufficient permissions.
The first thing to try would be to run the Backup Agent service with administrative credentials. Directions for doing this are here.
Secondly, consider using a scheduled task to perform the same action. Directions for creating a scheduled task can be found here.