Autocomplete: dropdown does not scroll with non-body container

The autocomplete dropdown does not stay with the associated text input if a container other than the page body is scrolled.

For example, put a text input within a tab control that has a scrollbar, where the page (body) itself has no scrollbar. If you dropdown an autocomplete for that textbox, then scroll the tab contents, the textbox moves but the autocomplete dropdown stays in one place. There should be a way to have it stay attached to the underlying input element instead of being absolutely positioned with respect to the body. It's possible the position option (http://dev.jqueryui.com/ticket/5153) would fix this, but it's hard to tell.

See example at http://jsbin.com/otozo4/2.