Hi,
I have the same issue. The whole plastic "belt" broke and fell off and the button along with it. I kept using it without the button though. You can still work the button, it just needs a push with a fingernail or something else small and a bit sharp (like a part of a bracelet perhaps, if she wears one on the same wrist). It's a hassle but it does the trick. My problem lies mostly with charging it cause without this whole plastic "belt" part the cable doesn't click so you have to stand there and hold it while charging - I still haven't figured a way to solve that one.
Mine was out of the 1-year warranty and I also bought it in the States but live abroad, so I haven't looked into my options on a replacement to be honest.