I get asked this question a few times a year. Right now I get this question every week or so. I always ask people why they want to fire a specific customer and if they know the lifetime value of that customer, or if they know the lifetime value of any of their customers.
Right now I get questions relating to customer who pay slowly. The economy is poor and many customers are hurting, you may need to revisit payment options or you may want to lose those slow-paying customers. Payment options might include, 2%/10, a straight monthly fee deducted from a credit card or checking account, or a penalty period.
American Express just released How To Fire A Customer in the small business area of their web site and they present pretty clear conditions and process for firing a customer.
But before you undertake any of the process they discuss, you must clearly understand the value a specific customer brings to you, whether that value is profit, proof of performance, or some other measure. Do your homework first and then look at whether this customer is costing you more than they are worth.
Just make sure that whatever direction you turn the result reflects properly on your business or you may find that it would be better to have kept that slow-pay customer.