The clock should be somewhat reliable assuming you have standard safeguards, such as syncing with a time server, and locked down to prevent accidental changes.
However, to mitigate any potential damage, consider adding another table that records each date that the records are deleted.
If your process runs weekly, then it would check this table to ensure that the current date is within a week of the last time it ran. This ensures that you won't skip any weeks, limiting potential "accidental" loss to a week. Adjust your window as needed.
If the check fails, require user intervention to get things back on track.