The main difficulties are the high per-transaction fees and the reasonably large percentage revenue cuts all of the concerned parties take from you. The more you charge, the larger the percent of your revenue you keep.
The smaller the granularity the more likely it is you'd need some sweeping change at the top of the chain -- at the CC providers, banks, processors. Most services charge you for every authorization request you initiate, let alone successful or failed transactions, so you'd have to be charging a very high rate for your service to be authing a card once a minute.
Not only that, but that many authorization attempts would immediately trigger fraud filters and the account would be locked.
Now I'm thinking, what would it take to reduce the payment granularity to 2 weeks? 1 week? 1 day? 1 hour? 1 minute?
I mean, we already have compound interest, which calculates interest continuously and precisely over time (I think). Why couldn't we have the same for payments?
Now I know that "micro-payments" aren't a new idea and it must be a really tough challenge but if someone has some knowledge of the different difficulties I'd love to see them spelled out.