Losing tufts of fur???

I just recently got two chins, one 9wk boy & one 2 yr old girl. The boy was from a respected breeder with many national champions, but the girl was from a friend who wants to get rid of many of her chins. She's black velvet & fairly friendly. When I let her run on the ground and then try to pick her up after play time, she starts losing a ton of fur, and my boy has never done this. At first I just blew it off but now she's getting bald spots where all of the fur has come out. I've read that in the wild they do this to slip away from predators. Has anyone else experienced this? Does anyone have any advice other than to just not let her out of my arms? And should I avoid breeding because of this? My boyfriend has bred them before, so he knows what he's doing, but he's never experienced this loss of fur before.