On Android 2.3, a fixed element that contains an absolute positioned element, which itself contains an absolute positioned element, will cause select menus on the page to stop responding altogether.

By removing that nested absolute element (represented by the red square above) the select menu will work normally. Alternately, by removing the fixed positioning of the parent element—either by not disabling user-scalable in one’s viewport tag or by removing the fixed positioning.

Edit: It seems this bug pertains not specifically to nested absolute elements, but to empty absolute elements—including whitespace. By adding a non-breaking space to the nested element, the problem is solved.