you are right, it is oil in the nail beds, there are some tricks to try to get polish to stay on longer, but honestly I have troubles with it even as an adult. There are some base coats that are made that make nail polish stay on longer like Creative Nail Design Stickey Base Coat. I don't know how "kid friendly" it is, but it works. If you give something like that a try I will warn you that it never dries and that's why it keeps polish on so long. Revelon has a similuar type polish set in the Colorstay line with the same premise, only the color itself doesn't dry and the topcoat does.