There are a few reasons to tolerate the customer who makes unreasonable demands:

• You promised you would
• She helps you raise your game
• Her word of mouth is very powerful
• The cost of frequently figuring out which customers to fire is too high compared to the cost of putting up with everyone

It's probably worth firing a customer if:

• He willfully corrupts your systems at a cost to other customers
• Your employees are prevented from doing their best work in the long run
• His word of mouth can't be changed or doesn't matter
• He distracts you from delighting customers that are reasonable

In general, organizations are afraid to fire customers, no matter how unreasonable. This is a mistake. It's good for you.