Okay, this is some BTDT (still doing it) advice for you, which may or may not apply, but I suspect that at least some of the underpinnings DO apply, given some of what you've stated.
My DD13 has been taking lessons for seven years. She, too, goes through periods where even getting her to practice for twenty minutes a day requires Herculean effort on OUR part. It's at times been misery. We've used a kitchen timer, the alarm of which has seemed like a starter's pistol as DD SPRINGS away from the piano bench. Not kidding.
Now, here is the part that I think that applies to us both.
1. Are you really sure that this is a "privilege?" Because that is how you (and we, at one point) were treating piano lessons-- as a "treat" rather than, say... something like allergy shots which is "unpleasant sometimes, but ultimately for your improved quality of life in the long term/big picture." Now, maybe it's all of those things... but if it's a "this is good for you" thing, and I'd argue that it is; then maybe this isn't a decision which IS the child's to make. They lack the life experience to KNOW whether or not they should quit.
2. If piano is a responsibility that YOU (parents) have deemed a priority, then be matter-of-fact about that-- practice is either negotiable or it isn't, or something in between...
3. Find out WHY your child is/is not into playing-- but know what is B.S. and what isn't there, and be honest about how much control you are actually ceding to him. My DD's favorite excuse is that her "hands hurt" if she plays longer than 15 minutes. Which is baloney-- because she is willing and able to use the ergonomic equivalent of "The Scream" on her computer keyboard to IM with her friends for four or five HOURS at a time, thank-you-very-much. Czerny isn't stressing her hands NEARLY as much as that must. The other excuse that we hear is "I forget to practice." Well, the answer to that one is routine-routine-routine; a morning SCHEDULE that allows for thirty minutes of practice to be tied to that scaffold (along with other chores and personal care, KWIM?)
4. What is YOUR goal here? Is it to foster love of the instrument? To foster a sense of personal responsibility? To teach that effort is proportional to results? To develop work ethic? All of those are worthy goals-- but they require different responses to the situation, certainly... our goals were basically weighted toward the end of the list because we don't have ENOUGH of those opportunities for our DD. Sadly, that means that item one is up for sacrifice if that is what it takes.
5. Different teacher? Is it that this teacher and your child are no longer a good fit either pedagogically, interpersonally, or musically? My DD has struggled with this one, since her teacher is a Baroque afficionado, and DD's interests are more along the lines of the 20th century Russians and Jazz improv... but the interpersonal fit is good, and frankly, any advanced teacher is going to kick her to the curb in a hurry given her mouthiness and lack of 'commitment' to practice.
Personally, I'd be reluctant to let a child determine how important this is. I mean, yes, ultimately it IS his/her decision in terms of how seriously they invest in it themselves... and that determines how well they play (or don't), how much they enjoy it, and the like. But it is about larger things than most children (even OUR children) can grasp at this point in their lives, since they lack something very important that we as parents possess-- perspective.
Quitting is easy. How many adults have you known who are glad that they quit and that their parents permitted it?
(Yeah-- me too. That gave me pause, actually, and caused me to rethink the approach that we'd taken up until that point. Our previous approach was much like yours. We'd tried making HER pay for any lesson that she hadn't practiced for, threatening to 'take away' this privilege if she didn't toe the line, etc. Rethinking changed that-- we battle over it far less than we used to.)
My feeling is that if DD tells me that she WANTS to quit... she needs to feel that way for {some period of time} before I'll consider it. That period is, for our family, six months. Her doldrums have never lasted that long, so she's still playing.
