Do saas apps typically bill for the upcoming month or bill for services provided during the previous month?
If it's for the upcoming month (charging per user), how do you deal with someone who has a variable number of users? If they drop users mid-month and you credit them for next month, it will seem to them that they are being charged after the fact even though they aren't.
I suggest you deal with this in your legal documentation (service agreement/contract). Personally I would bill up-front as that's better for your cashflow and most services out there expect you to pay before you use.
I wouldn't worry about customers feeling bad that they have to pay for part months for users that drop off mid-term (unless of course your per-user fees are huge) - just put it clearly in your legal doc and in the sign-up page that you are paying per user per month up-front and that there are no refunds for any unused part-months. I am assuming you are letting your users cancel at any time - if so, I would say this kind of payment structure is pretty common for SaaS businesses.
If you can avoid operating a credit system, I would - there's nothing worse than not being able to account for your income because you may have to give some of it back.
All this is said in the context that you are providing your customers with a valuable service that is well-run and they get good support - if these things are in place, in my experience, people are happy to pay fairly and don't usually get involved in penny-pinching.
As a rule of thumb, recurring fees up-front, usage-driven in arrears.
The question over users dropping out mid-month, I'd try and avoid rather than resolve.
As long as you have sensible customer service in place, you'll get to hear how many customers have an issue with how things work out. Go back and talk to the people who had a problem and get underneath it. Ask them how they think things should work. That way, you can either refine your policies to deal with this issue case-by-case, or you can automate what emerges as best for your customer and manageable for you.