It's either one of two things...
1) Your children's personalities...maybe they aren't dog/pet people.
2) They just aren't old enough for a dog yet.
We just got our second dog. Actually, my daughter adopted him using her birthday money. My children are 15 and almost 13, and they PLAY with the dogs. We are having the best time ever, and I think it's because my kids are old enough to know understand the dogs' moods. They want to help take care of them...most of the time anyway.
Again, I'm sorry. I know that is really tough. We get so attached to our pets. I don't know if you are a person who prays, but if so, try praying for an answer. Perhaps the perfect person will come along. Or, perhaps you are meant to keep the dog for an as-yet unknown reason.