Honestly ask them if they really want to go camping any more. They are at the age when kids really start seeking their own independence. If they say they do not, then leave them home. One of two things will probably happen. 1) They will feel left-out and a bit "lost" without parents home, and realize they have to do things themselves, they will want to go with you the next time. Or, they will enjoy their new freedom and want to stay home alone always. Either way, you need to respect their changing needs. Your camper, your home, your job, your lifestyle ... is just that ... "your's", not theirs. They need to be let loose a little so they can discover what THEY are wanting for their lives. Camping may not be one of them.
When our kids turned 15, they no longer camped with us. When they turned 16 they were both working part time jobs. They didn't have time for Mom and Dad any more. Now, we are grandparents of 5 kids. And yes, because we did give them the liberty to make choices themselves, huh!... well ... my son and his son are living with us now ... can't get rid of them, and they occasionally, when work permits... they go camping with us! Imagine that!