Does the event CE holds the same effect on the same events on their next return or re-run.

The return of nero fest basically this is the last event for her right? Might get a re-run from 3 yrs now or so. So my question is does any first event that with chance of return or re-run can use the same CE and does have the same effect or apparently every new event or re-run will have new CE no matter what.