Simply head to the Settings Page of your Live Study, further down the page, you will see the ability to edit the completion date.

The Recruitment Team will continue recruiting & managing your Study based on this end date OR if your quota gets filled before the end date.

Your Study may remain Live or Active even if the end date is in the past, this normally means you quota has not been filled before the end date.
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To continue getting the rest of your responses, just update the end date & invite more people!