I've been using Stripe for just over a year now to take payments for a 6-figure-a-year business. We've had no reversals whatsoever. The only time Stripe has removed payments have been in the case of the occasional chargeback, which we typically win; payments seem to get docked the moment you file your response to the dispute, and get credited back the moment you're notified the dispute has been won.
I was a little nervous when first setting up with Stripe too, so we enabled it for a few hours and let a few sales go through, then switched back to our old merchant account and payment gateway while we waited to make absolutely sure the sales went through with Stripe. 7 days later, the payments hit our bank account, and we switched everything over to them - been happy ever since. They have a great dashboard, and everything's far easier to deal with and manage than it was with our old merchant account. Only downside is the pay delay - merchant account deposited most funds in our accounts within 2 days; Stripe takes 7. But if you're doing pretty consistent numbers, this isn't too much of a burden to cash flow, since you've got the funds from a week ago coming in every day.