Extending the deadline of an ongoing survey is easy. To extend the deadline of a survey, find the survey on your 360° Surveys page. Press the "Edit" button, enter a new deadline and hit "Save". You will be asked if you want to send notifications of the changes. You probably want to say yes so that pending participants are informed. People that already submitted their responses will not be notified.
Find the 360 survey you want to extend the deadline for:
And modify the deadline:
Note that you can also re-open a closed survey by editing it and setting a new deadline in the future.
If you need to update more than one survey's deadline at a time, you can also use the Batch Operations functionality as shown below.