Apparently you can still participate in the events after they end...provided you started it before the deadline.
I didn't start the recent Snake Bananza event until yesterday evening and people were correct when claiming it was tough. After multiple attempts, I was resigned to not getting either statue because I had failed to rank high enough and it was already past 1 AM on the 19th. Imagine my surprise when I could select "Lemme try again" after the results screen and it let me retry the event! It seems you can indefinitely retry the event past its deadline as long as you don't exit it (i.e. don't return to DK Island or exit Emerald Rush).
I reached a point where I had to go to bed, so I put the game in sleep mode and continued later in the day. Eventually I was able to get both statues (thank goodness).
Hopefully this workaround or exploit or whatever you want to call will help some folks who get a late start on one of these events.
I apologize if there was already thread about this but I couldn't find it.
A final note: I'm not sure what would happen if you kept playing an older event once a new one starts.