I realize this question is dated, however it didn't help me 100%. Below is the solution I came to after some refined googling, decided to post it here as this was my first result.
My problem was that the header and footer would hide when tapping an input, regardless of whether the default behaviour was used. I was using the amazing DateBox.
Manually updating the DOM header/footer with data-tap-toggle='false' didn't do anything, but this would have saved me some time:
$("[data-role=header]").fixedtoolbar({ tapToggleBlacklist: "input[data-role=datebox]" });
$("[data-role=footer]").fixedtoolbar({ tapToggleBlacklist: "input[data-role=datebox]" });
For whatever reason, disabling tap toggles this way solved my issue as well as showing me a short-hand for disabling it across a large number of pages.