Well I seriously had not this experience with myself..
But here I have one question are you sure you have this problem due to mask..
Just try to remember about the past were you falling any problem before the mask..?
It might be possible your molars become weak and something like this ..

I didn't use this chin strap for myself.. But I think its not a big issue you just consult with your doctor first and.. verfiy about the chin strap size for yourself what doctor recommends..
And then you can try to buy a chin strap for yourself from anywhere..