I think that under $10,000 a week by itself should not trigger a SAR.
You did not say what industry the customer is in - perhaps the volume is consistent with the nature of the business...?
You also mentioned that you have filed numerous SARs..
Your policy should state that you will close the account after a certain number. For example, a lot of banks will draw the line at 3 filings.
So assuming the cash does not fit the line of business and is therefore suspicious, - and if you have a cut off number for filings, that would be the end of it... You would then close the account.
Going back to your question of should you continue to file SARs, I think the answer is No, ..you should be closing the account if you think the activity is suspicious, and further you should have your policy updated with the maximum number of SARs that you will file so you can put closure to these scenarios.
An additional comment - I think checking tax returns to cash in etc is above and beyond the call of duty. My humble opinion.