As you'd expect, this was obnoxious. Finding the solution was a bit annoying, too, as the most recent post I found, from 2009, Which, as you might expect, wasn't helpful. However, I did get it figured out.
- Go to www.YouTube.com/my_videos. This will give you the master list of all your videos.
- Skim through to the video in question, click "Edit".
- Go to "Advanced Settings"
- Scroll down to "Distribution Options" & Click Allow Embedding"