There are two Task Scheduler specific services and these need to have the correct Status and Startup Type parameters set in order that the Task Scheduler will start itself after a reboot.

 
The correct settings are:

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'TAW_TaskScheduler(<machinename>#<database>)' service
Status:  'Started'
Startup Type: 'Manual'
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'time@work TaskScheduler' service
Status:  (blank)
Startup Type: 'Automatic'
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These settings are in place so that the time@work TaskScheduler service is started with a startup of the machine and it then calls the other service.