You could set up an event log alert for the service stop event, as ict-user suggested as well, or create a report that lists stopped BestSync services and set up a report alert for this. Instructions for setting up email alerts can be found
here.
As for automatically restarting a stopped service: you can use the deployment module for this. If you create a report listing machines whose service is stopped, you can run a scheduled deployment on this report to restart the service. General instructions for creating and running deployment packages can be found in
this section of our knowledge base.