You may wish to inquire with 2CO if they have a setting for more strict verification of billing information during checkout before they authorize the payment, rather than doing so afterwards or waiting for a cardholder to file a chargeback claim for a fraudulent charge on their card (e.g., due to stolen card details).
That latter scenario is probably what is actually happening when you get payments canceled some time after the original checkout was completed, so that would not be solved by waiving the requirement to enter billing information -- cardholders would still file claims to void charges made to their card by unauthorized parties.
At any rate, checkout is handled entirely at 2CO's end, so aside from sending the order details to them in the first place, we have no control over how they handle checkout or process the actual payment; you would need to consult their help pages or support team regarding what options and settings may be available to you at their end.
