What happens on menu item click when the gantt control is inside the UpdatePanel:
1. Do you see a full page PostBack?
2. Any JavaScript error?
The UpdatePanel should intercept the PostBack calls and invoke a partial PostBack instead.
It looks like you display the modal dialog using the ModalPopupExtender. It might not be the solution you expect but you can use the DayPilot.Modal helper to display the modal dialog. It displays a standalone page (unlike the ModalPopupExtender) in the modal window. This is solution is easier to debug.
See also:
http://code.daypilot.org/81367/daypilot-modal