Yosemite Messages Screen Sharing Disabled

I'm trying to screen share on from within the Messages app with another iMessage user. We're both on Yosemite, and we've successfully used Messages's new screen sharing feature many times. One day, we discovered the screen share button was disabled. It has never come back.

Screen sharing is enabled in the Video menu, and we are both on the most recent version of Yosemite. I'm not sure how to look for answers without even an error message to go on.