Depends entirely on the problem(s) that sent her to therapy in the first place. My answer for a kid who is just having some trouble making friends is different than for a bipolar kid that is suicidally depressed.

Its never as simple as a yes/no question. And unless you are in a situation like that, you couldn't possibly imagine what you would do.

And yes, this is coming from someone who has been in this situation. I'm not going to discuss it in this forum, but I just wanted to state that for the record.

I agree with the comments above, but I'd also add that there are treatments that are much more effective with a participant who wants to be part of the process.
Also, the way you phrased it makes it sound like it's probably not a situation where the patient is a danger to himself/others. If s/he isn't, I give a tentative yes, my child can quit therapy.
That being said, I'd try to get to the bottom of WHY the child wants to quit. If it's something like an issue with the therapist, as someone else suggested, that's something I'd want to know about so I can look for a different therapist.

I agree with this one.

It depends on the child's reasons for not wanting to go anymore.

First, I'd talk to my child and find out why they want to quit therapy. Perhaps the problem is with the particular psychologist, and switching psychologists would be the key. Failing that, I'd let them quit therapy regardless of what any (QUACK!) doctor has to say about it. The possibility would exist that my child may not be ready to deal with his/her issues yet. In that case, forcing can cause more harm than good.

Depends on what he/she is seeing the therapist for.

Depends on the problems. and on the severity and kind of reason why s/he is in treatment.