You absolutely should not have duplicate IDs. It may work*, but it is semantically incorrect and you should not do it
You should restructure your jQuery, however much that may stink. The best option would be to use a class, perhaps using the specific id of the parent to specify which one you want
Another less attractive but viable way would be to add a number or something to the end of the ID to make it unique then use jQuery to detect any elements with a specific part of an ID
* – As Arun describes jQuery will accept the selector, but it is NOT favorable because it is incorrect