Thanks for your post. SQL Backup relies on the SQL Server Agent to be running in order for a scheduled task to be run.
Unless you're using Task Scheduler and calling an executable from the command line, any sort of scheduled job running in SQL Server relies on the SQL Server Agent to be running.
I'd therefore take a closer look at the SQL Server Agent and see why that's stopping, as to the best of my knowledge it shouldn't just stop through inactivity.
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