why are my shortcuts to homescreen lost everytime I power my phone off. when I power my phone back on, their no longer there anymore

I did some searching about this but did not find a really clear answer about what causes it. However, I don't think Firefox is removing them. I suspect it is an issue with your home screen launcher, which could be the standard Android launcher, or one customized by your device manufacturer, or Google Now cards, or a third party app. If you don't get a satisfactory solution here, please try a more general Android forum such as http://forums.androidcentral.com/ and maybe test whether the same problem affects home screen shortcuts you create using Chrome or your device's native browser to see whether those have the same issue or are immune to the problem.