Here's the response I received from support:
The value is not preserved because of the autocomplete attribute used
on the text input. In order to preserve the text, you could change the
attribute value through code after the combobox initialization:
combo = $(
but please note that this would also enable the browsers
default auto-completion which may cause two popups to be shown when
typing - one from the browser and one from the combobox.
I tried that and I indeed saw the two popups, which is not desirable. However, the behavior is not all that reliable. Sometimes my combos retain their values just fine and sometimes not. It's unfortunate that the combo behavior is so non-standard.
I hope this helps get you closer to a workable solution.