FaceTime video message not received by recipient

I tried a video calling my friend and she did not pick up. At the end of the call, I was given an option to record a video message, which I did. I then hit send and thought my friend would get this message. It was important. It seems that my friend never received this message or got any notification of it and I cannot find a recording or a trace of it anywhere. What happened and how can I fix this?

[Re-Titled by Moderator]

Original Title: FaceTime recorded messageissues.