With the above insight, once I *disabled the above add-ons* on my local instance and copied the Youtube Link such as https://www.youtube.com/watch?v=k6lK5hlB1nQ(https://www.youtube.com/watch?v=k6lK5hlB1nQ) (must be copied from the Browser URL, I assume it picks up additional metadata it's a URL and not a text string) and pasted into my Confluence page, I could replicate the issue!
As you are currently on Confluence 6.15.2 which has a fix for both the [Confluence Security Advisory - 2019-03-20](https://confluence.atlassian.com/doc/confluence-security-advisory-2019-03-20-966660264.html) and [Confluence Security Advisory - 2019-04-17](https://confluence.atlassian.com/doc/confluence-security-advisory-2019-04-17-968660855.html), it is safe to re-enable these add-ons that were disabled prior upgrading to 6.15.2.
Can you please try the following:
1. Navigate to *Confluence Administration* ยป *Manage Apps*
- Change the Combo box filter to *System*
- Re-enable these add-ons
> * Office Connector plugin
> * WebDAV Plugin
> * Widget Connector
You may need to restart Confluence if the page edit still doesn't work. Let us know if that does the trick and stops the pasted URL disappearing!