Well often the community as a whole will take care of the 'trolls' (as they are called), but if your community is not loyal or not strong (active) enough there are a couple of tactics to take:

"Kill them with kindness." Nothing looks worse for a troll than a company doing their very best to appease his requests.
Outline the problem in great detail publicly (on Facebook, twitter, etc.) and resolve with as much care.
If you can always overtly familiarize the troll with product or service.
If they're being slanderous (privately) extend a very polite and legal cease and desist - he may post it publicly so it's important that you're not threatening in any way.
Show them your SocialMedia SOP (or create one) and insure them that you're speaking to them honestly.
Unless completely profane don't remove the posts; it will just fuel their fire.
Click through to their Facebook profile and go down to the lower left hand corner and "Report/Block This Person" and detail the reason if need be.
Assign him a "shrink" - this is a social media expert that will work one-on-one with the person to resolve the issue if there is indeed a way to resolve it.
If all else fails and they've made you a "hobby of hate" you can sue them for "Tortious Interference" - when a person intentionally damages the plaintiff's contractual or other business relationships. This is often hard to prove, but to your credit you'll have had all the posts to reference with digital time stamps. If you can prove a legitimate association to dropping sales or negative feedback during the time of the individual you [might] have a case.