One of the most common headaches when making CSS for mobile, is the inconsistent, buggy and awful implementation of position:fixed;
There's a lot of resources explaining this, so I'll just throw a bunch of links instead of writing a new post about it.
The problem (iOS)
Issues with position fixed scrolling on iOS - Remy Sharp
The problem (cross device)
Mobile fixed position - Brad Frost
How it should behave
...and it does on modern mobile browsers:
Budding consensus on mobile position:fixed - Peter-Paul Koch (PPK)
Test page
Just CSS, no JS fixes applied.
position:fixed test page
The 'fix'
I think quite all alternatives are explained on Brad Frost's post, so I'll link again to it:
