The problem comes when you get paid for 6 and you work for 2 hours or for 18 hours. One party or the other isn't happy with that.
I can see that.
From the point-of-view of the attorney that put in 18 hours for something which he expected to take 6, that's 12 hours he could be billing on another matter. Or going home early. Sure, I'd be unhappy about that.
From the point-of-view of the client that saw 2 hours on the bill when he expected 6 ... is the client dissatisfied with the arrangement even *if* he is completely satisfied with the work product? Why does he care that the law firm made more profit than expected?
Does the client's dissatisfaction stem wholly from the idea that he paid more than he had to?
But that's how business works, sometimes you do very well on a deal, other times you lose money. If you're not comfortable with that, then you are better off working on an hourly basis.
In my experience, flat fee arrangements are more common with volume work. You win some, you lose some, but the plan is that it all averages out so that both sides are satisfied. Without the volume, you can end up with one side winning and the other losing.
So I agree: If either side is dissatisified, the parties should re-negotiate the price or terminate the fixed fee arrangement.
Unless the reason the attorney took 18 hours is due to inefficiencies with him/the firm, rather than client-related issues (e.g., complexity of the work, more back-and-forth with inventors/inhouse counsel than expected). If the former, then the attorney should consider whether he can reduce these inefficiencies so that the work is as profitable as initially expected. If not, the attorney should re-negotiate or move to another arrangement.