You will need to upgrade to
DayPilot Lite 2.3. Previous versions are not compatible with UpdatePanel.
I see that you have modified the source code for your needs. It's necessary that there exists an element with the DayPilot's ClientID (i.e. you will need to add id="" attribute to the main div) on the page and that the event delegates use the standard parameters - i.e. (object sender, EventArgsDerivedClass e). Without these two modifications UpdatePanel doesn't detect DayPilotCalendar events properly.