Ok, I added this to your Custom CSS page (which can be found on the Customizer page in the “Additional CSS” tab) –
.site-header.shrink {
position: relative;
}
This is one of the things that will prevent the header from being “sticky”. There’s more code in the background, but we won’t need to touch it since the code above prevents it from activating.
I just pulled up your site on an iPhone using the Chrome and Safari browsers and everything looks good.
Unrelated: The only thing that didn’t look right was the Site Title/Logo. On an iPhone the text is too long so it gets cut off due to the screen size. I just added some code in the Customizer CSS that shrinks the font size on any device that is 480px wide and below –
@media only screen and (max-width: 480px) {
.site-title {
font-size: 20px;
}
}
Let me know if everything looks right once you take a look.