As someone who used to process hundreds of subscription payments and we did use QuickBooks Merchant as well as Stripe due to multi currency, I can only give you my experience.  

The majority of my monthly subscriptions processed would decline for new clients only, I had to create a welcome email to new clients requesting that they contact their bank and authorize payment.  A lot of banks now have this security feature and client doesn't even realize it.   If payment card number information is correct and still declining, here are some possibilities :

1. The client/customers bank is blocking/not authorizing payment - they must call themselves and approve the transaction.
2. The address does not match the card (this was a common issue, some clients don't even realize especially if the move/travel frequently)
3. Wrong name on account (also common, a client/customer would use a spouse or relatives and in that case must submit an authorization form from that person on card/account)
4. Client/Customer card is out of country, almost always requires authorization directly from client/customer.
5. Client/Customer has a set spending limit and must authorize amount if over. 

To run a card correctly, you must have Authorization, be within their Spending Limit, correct Name, and Correct address.  Banks have a lot more security on their cards these days.  It is best when possible to send client/customer an invoice and let them pay directly through invoice.