Remove Post after set time

There isn't any way to set this in Gravity Forms.

You could look for a plugin to automatically expire posts after a certain date, or use something like this where you create a custom page template for your posts then add a custom field value via the form for the expiration date. You should be able to populate the custom field value dynamically. It would still involve some creativity to make it happen.

http://www.wprecipes.com/how-to-set-post-expiration-datetime-on-your-wordpress-blog

http://wordpress.org/extend/plugins/post-expirator/