There is a new feature to set an expiration date for Video post on Facebook's page.
You'll need to allow expiring posts on your Page to schedule an expiration date for a video. To allow expiring posts on your Page:
Click Settingsat the top of your Page
Click Expiring Posts
Click to check the box next to Allow people who manage this Page to select a time when posts unpublish
Click Save Changes
To schedule an expiration date for a video on your Page:
Add a video at the top of your Page's Timeline
Click drop down arrow next to Publish and select Schedule Post
Click Schedule Expiration Dateto turn on video expiration
Choose the date and time you want the video to expire
If you want to delete the post when it expires, click to check the box next to Delete the post. Permanently remove the post and its insights at the scheduled time.
To schedule an expiration date for a video that's already published to your Page, hover over the post on your Page’s Timeline, click in the top-right corner, and select Schedule Expiration.
When your video expires, it won't be visible on your Page or anywhere else it was shared on Facebook. To see a video after it expires, click Publishing Tools at the top of your Page, then click Expired Posts.
Keep in mind that if you choose to delete the video when it expires, the post will be permanently removed from your Page, your Page's activity log and insights, and anywhere else it was shared on Facebook.