It's very common for kids, usually about the time they reach the middle school years, to begin to temporarily lose interest in lessons. If they are allowed to quit lessons, they usually regret it in later years. It is possible to get your children through this difficult period without having them make a decision they may later wish they hadn't made and for which their young age and limited experience ill prepares them. I firmly believe that, while kids say they know what they want at Jr. High and High School levels, they really don't know exactly what they will be missing by quitting the study of musical instruments. I have had many adult students who kick themselves for having quit and now realize the folly of their choice made as teenagers or as children.
One thing that often works well in keeping kids in lessons is a tit-for-tat agreement to continue lessons in exchange for some privilege or reward (sometimes known as"positive reinforcement: sometimes known as a "bribe"!) Such rewards need not be monetary or material. For example, a possible "contract" might be allowing your child (daughter) to get her ears pierced in return for her continuing lessons for 3 more years. Similarly, you can reward good lessons and participation in recitals and concerts, help show your child how supportive you are of their efforts.
Whatever reward system you choose, make it clear to your child that this must be a good faith agreement between you, the parents, and your child. Regular practice and attendance at lessons are every bit as important to the child's fulfillment of the contract as you're allowing the privilege. For this to work, the child has to know that if they "welch"on their end of the contract, you will not trust them in similar situations in the future and they will lose those privileges they might otherwise have gained. Such an arrangement not only helps keep your child in lessons, but also builds character and responsibility for their future.
Despite your best efforts, your child may refuse to cooperate. Should you force the child to continue lessons? Every situation is individual, so I can't tell you what to do here. However, in this event, careful consultation with the child's teacher is called for. The teacher may be able to rebuild interest by changing repertoire, using computer teaching tools, setting up opportunities for playing in groups with other children the same age, or other incentives based on the teacher's knowledge of your child. Simply allowing the child to quit lessons is usually not the best way to handle a resolutely uncooperative child. Such a decision should only be taken as a last resort and involve extensive consultation with the teacher.
Finally, words just for you parents: hang in there, it's worth it! Give yourself a pat on the back that you recognize and are dealing with the issue. Chances are your children will thank you when they get a little older for encouraging them to stay in lessons.