Do you believe it's okay to fire a customer?

Customer is King
Always Treat them like King and you will get the fruits of your Loyalty.

No, its not wise.

I agree with everyone else, it is at times best for your company, your sanity and usually in the clients best interest as well.  

Yes. Only after you have done everything knowlagable to fix their complaint and worked with their solutions to limits allowed by your business.I suggest asking them to continue using your services as needed in the future but with appoligies suspend them from access with a set time frame .

Yes, if they are too way demanding or disrespectful or too hard to please, it's best to just cut ties..

YES! You can't make everyone happy and if that client is taking business or time away from you or you are always stressing about them when they come in, it's time for a chat.

Just like in any other relationship if it is unhealthy, it is not wise to continue it. But we have to be diligent and self aware enough to know, that it is not us that is the unhealthy part of that relationship.