This is a difficult problem to get 'right'. You can try and hide the footer on input element focus, and show on blur, but that isn't always reliable on iOS. Every so often (one time in ten, say, on my iPhone 4S) the focus event seems to fail to fire (or maybe there is a race condition with JQuery Mobile), and the footer does not get hidden.
After much trial and error, I came up with this interesting solution:
<head>
...various JS and CSS imports...
<script type="text/javascript">
document.write( '<style>#footer{visibility:hidden}@media(min-height:' + ($( window ).height() - 10) + 'px){#footer{visibility:visible}}</style>' );
</script>
</head>
Essentially: use JavaScript to determine the window height of the device, then dynamically create a CSS media query to hide the footer when the height of the window shrinks by 10 pixels. Because opening the keyboard resizes the browser display, this never fails on iOS. Because it's using the CSS engine rather than JavaScript, it's much faster and smoother too!
Note: I found using 'visibility:hidden' less glitchy than 'display:none' or 'position:static', but your mileage may vary.
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