I have noticed that little icons I have put in the theme for social links over the navigation stop working at mobile sizes. They are build using image replacement. Is this something your theme might do? If it isn’t just let me know and I will try to figure out what I broke on my own. http://www.app-promo.com/beta
Pure theme custom icons as shown in demo do work on all android and iphone phones we have tested.
If it is your own custom code at the top of the page your question relates to, then this is outside of our control and strictly speaking therefore outside the scope of support we can offer. But yes image replacement can work on mobiles – no reason why it shouldn’t.
It would be difficult to guarantee behaviour on every device on the planet though, and part of responsive design is recognising that not every device supports every feature, but that doesn’t mean you should design for the lowest common denominator.