It's heartbreaking when your kids don't see the point of getting an education and ask "Why should I?" You know "why" because you've had enough life experience to understand the big picture and they, by definition, simply haven't and don't.
If your kids are giving up on learning, then its time to raise some (or some more) heat at school. Respectfully, constructively and effectively. This means go meet with the teacher, then the counselor and then the administrators. Talk with the PTA and go to the school board if necessary. Document everything, from whatever is or isn't happening in the classroom, to the content of your meetings. Expect resistance and all manner of bad behaviors, but take the high road and be tenacious. Be wary of easy answers, they can easily distract you from more complex issues and end up causing more problems down the road. Remain mindful of your thoughts and emotions, and dedicate yourself to constructive outcomes.
Be optimistic. Sometimes resolution comes very quickly and reasonably, and then everyone feels good. Be realistic. All too often, resolution doesn't come when it should. Then, the key is figuring out what the various players care the most about and then helping them realize that doing the right thing is the best way to get what they want. Do not let schools bully you, and believe me, they know how. Be fierce when you need to be, and firm, but always retain your integrity.
Do everything you can, within reason, to support your kid and encourage learning. If school sucks, then try to find ways for your kid to learn more at home. Investigate alternative schools and even other options, such as taking courses at community colleges. Try to find allies at school who can help you with "the system" and remember to be gentle with members of the school community who are caught in impossible situations and still try to do the best they can. It may not be enough, but they haven't given up and deserve our gratitude.
Finally, here's a suggestion should your kid decide "I'm done" and drop out, either from high school or college. Evaluate the situation, and if this decision is internally logical for your kid (and it's been a long time coming), then don't fight it. Usually, their decision comes from frustration, too many demoralizing experiences and the perception that education is irrelevant. Sending them back to class won't help.
Instead, make a deal (assuming your circumstances permit it). Here are the terms. You give them three months where you'll feed, clothe and care for them while they live at home and pursue service. Support them in finding a cause or group that means something to them (a calling from the heart) at which they can get a full-time internship or volunteer position for four months. No sloughing off.
Then, after one month, ask them to tell you about the challenges, needs, problems, and issues of the cause they're serving. Ask them to tell you what could "make things better" and who could have a real role in making those changes. What do those people (the "who") need to succeed? Money, sure. But which skills? What about education? How much? What kind?
After another month, start preparing for what happens when the four months are over. Realistically, there are two options: does your kid want to get a menial job for (close to) minimum wage or would it make sense to go back to school to get the education needed to do something for the cause?
Given this experience, almost all kids want to go back because getting the degree, and even more importantly, learning certain skills and knowledge, is necessary for doing what they really want to do. Education becomes relevant when you need it. The process might still be frustrating and certainly imperfect, but the biggest difference is motivation. When your kid had no cause to value the process or outcomes (and the system failed to instill these values), there was no reason to persevere. Once there is a reason - a need - well, that changes everything.
What's the true catalyst? Service. It's that magic that grows within us when we care and give. That's what causes your kid to see that education is a means to doing something bigger that feels good because its bigger than just him/herself. In my opinion, the most profound failure of education today is that it emphasizes and isolates the individual, so when education fails, the individual also fails (and all of us, by extension). Authentic successful education leads us to be more effective and burn brighter. More than knowledge or skills, it's our relationships, and the experience of compassion, kindness, and loyalty, which stoke the flames.