If you billed fixed rate and the client changes the requirements, then you change the fixed rate.
Say you estimate the cost at $10,000 and they want you to make a change, you say, "Okay, but this change wasn't included in the $10,000 so we will have to estimate how much the change will cost and add it to the bill. If you want us to do that, let us know."
This is why you have to outline the requirements before you do a fixed bid.
Instead of saying it's going to take 4-6 more hours, you say it's going to cost $400-600 more dollars, assuming you estimate at $100/hr. If it really takes you 1 hour, then you still make $400-600, but it only takes an hour so your hourly rate just went from $100 an hour to at least $400 an hour.
If you're a highly productive programmer and use the right tools, then a fixed bid can come out in your favor if you estimate projects using the hourly rates and estimates that not so productive programmers use.