Though who knows what Selebus has planned for the future? That day counter has always been wearing away at me in the back of my mind the whole game, as I wondered if in some future update time would catch up to me...There's no cut off date, and no worry of missing events by not getting to them in a certain number of days. (There are a few missable events, but not based on time.)
As of now the only thing the day counter does is that there are some events that will only trigger after a certain number of days have passed.