How do you set a close time for submissions?

If I understood you correctly you want to disable your form at specific time, so that your users are unable to submit it. 

Here are the steps how to set "Expiration date" on your form:

1. Open your form in form builder and click on "Setup & Embed"

2. Click on Preferences.

3. Select "Form Limits" tab.

4. Here you can change the "Expiration date" property of your from.

Inside of this guide you can also find how to limit submissions in a form:

http://www.jotform.com/help/137-How-to-Limit-Submissions-in-a-Form 

Hope this will help. Let us know if you need further assistance.