Howdy,
I had a similar issue (on another site) with a prepaid card that my (soon-to-be) mother-in-law gave me. Unfortunately, banks govern prepaid cards differently than normal cards. With a linked bank, debit or credit card, they can adjust the transaction if there are any concerns and can refund without concern. With a prepaid card, they can often be one-off payments and the card destroyed. For this reason, anything that might require a refund or adjustment is suspended--which means a lot of transactions cannot be complete.
Further, here is what Braintree says on the subject:
"Braintree can process any card that bears a major card brand logo (Visa, MasterCard, Discover, JCB, Diners, AmEx) regardless of whether it's considered prepaid or a gift card. Banks aren't always as open-minded. Even though we can process them, this doesn't mean that the banks will allow the transactions to go through. Prepaid cards might run successfully on one-off transactions but are often declined on recurring transactions."
Here at Shapeways, we do come across the case when a model cannot be printed (though we try really hard to print them all). In such a case, the ability to refund back to the original payment method can be essential. Therefore, it may be in your best interest (despite what the bank says one way or another) to go with a more secure type of payment that will allow you to get that refund if any issues come up with your order.
Also, feel free to open up this dialogue with us here at service using the webform so we can start you in on that order. That way, we can discuss details that you might not want to discussed in an open forum.