My subscription renewals fail with error message "Customer action required" what can I do?

This "Customer action required" or “CUSTOMER_ACTION_REQUIRED” message comes from the payment processor and indicates that the payment processor or the customer's bank has requested an additional verification to process the charge. This is a part of the so called 3D secure verification, which usually protects the merchants against chargebacks.
Generally, this should rarely happen, as banks remember that the customer authorized your shop for future charges, which means that renewals of subscriptions should go through without any issues. 
But if this happens often, then there is probably a setting turned on at your payment provider, which requires this additional authentication.