Stolen cards, for instance, which may be more likely to happen in some industries than others.
While I understand the need for ambiguity with respect to your business operations, this post is too vague to give any understanding as to why Stripe blocked your account.
Once you have a card you can absolutely take arbitrary amounts of money from it, and this appears to be their suggestion. It could well be that they are using (purposely) vague wording that confuses people about their charging structure (in one off payments or subscriptions) which generates complaints to banks and then Stripe have to deal with it. Or it could be a big misunderstanding Stripe side and they have done nothing wrong. I have an opinion on which one I think is most likely.
Charities also have huge problems with CC fraud, as they're seen as an easy target to test card details against before making the "full" purchase elsewhere:
http://www.bankinfosecurity.com/stolen-cards-tested-on-chari...
They get upset about it anyway, because Visa/MC mandates it. A reversal ratio above ~1% threatens Stripe's ability to act as a processor. A bit of Googling will turn up plenty of people with terminated accounts for excessive chargebacks, just the same as any credit card processor.
Actually, you do. In many cases, fraud follows a pattern. If you're a merchant, and you're getting a lot of fraudulent charges, you'll often get into a discussion with your upstream processor's fraud department about the details and how to mitigate it. I don't work in payments anymore, but as an example of how this works, I was talking a few weeks ago with a merchant who does tens of millions gross every year, but also faces five digits of fraudulent transactions. They sell car parts, so it's quite easy to buy one or two things for a lot of money. While working with their processor, they discovered that a significant amount of fraud was coming from two cities. And not just two cities, but two neighborhoods. And not just two neighborhoods, but two streets.
They simply reject any transaction from that street before even sending things to the processor, and now they're saving tens of thousands of dollars a year.
Preventing fraud is the most difficult part of payment processing; are they outsourcing it to the merchants?
You know your customers and business better than anyone, even your own upstream.