Yes. You can change your unmoderated study's completion date at any time, including after the date has already passed. Updating it retroactively reactivates the window for responses to come in.
Where to change it
On the older layout, open your live study's Settings page and edit the completion date field part-way down the page. If your study uses the newer studies experience and you can't find the field, message us on live chat with the study title and we'll update it for you.
How the date interacts with recruitment
We recruit and manage your study against this end date, or until your quota fills, whichever comes first. A study can stay live past its end date when the quota hasn't been filled; to keep collecting responses, push the date out and invite more people.
The due date is not the task timer
Two separate clocks apply to unmoderated studies:
The completion date is the deadline for your study overall. Invited participants can start the task at any time before it.
The 120 minute limit starts when a participant begins the task; they must finish in one sitting. See Why is there a 120 minute time limit?
Extending the completion date gives more people time to start. It doesn't give anyone more than 120 minutes once they've begun.

