It seems that the problem is that this is not a standard pure CSS dropdown menu, as one might assume. Instead, it's been controled by jQuery. You can see it in the app.js file:
$('.nav-bar>li.has-flyout').hover(function() {
$(this).children('.flyout').show();
}, function() {
$(this).children('.flyout').hide();
});
So you should modify the script in order to work with a touch for selected devices (there is a good discussion on that topic here). Here I am using a simple statement. I have not been able to test it in iPad, but you could have good results if you try to use something like (untested!):
if (navigator.userAgent.match(/(iPod|iPhone|iPad)/)) {
$('.nav-bar>li.has-flyout').bind('touch', function() {
$(this).children('.flyout').slideToggle();
});
} else {
$('.nav-bar>li.has-flyout').hover(function() {
$(this).children('.flyout').show();
}, function() {
$(this).children('.flyout').hide();
});
}
This should give you some clues on how to deal with that. Let us know if it works.
There is also a lot of information in this stackoverflow discussion about hover and touch devices.