An expiry date for a Challenge acts the same as an expiry date for anything else. Once it's reached its expiry date, the Challenge will no longer be available to the public.
Players can still view the Challenge, but they will not be able to complete it.
To add an expiry date to your Challenge, on the Topic Manager page, decide which Challenge you'd like to add an expiry date to, and click on it.
Scroll down. Under the "Other Options" tab, you can add an expiry date to your Challenge.
Do note that once a Challenge has expired, there is no way to make it active again.