Frozen and fuzzy video during FaceTime calls on iMac

We FaceTime my cousin in Australia every fortnight, but for the last six weeks have had a problem with visuals. Throughout our call we have a perfect visual display of them and excellent audio. At their end they have excellent audio, but after a few minutes their visual view becomes frozen and fuzzy, and usually stays like that for the remaining time of our call. Is this likely to be a transmission problem at my end, or a reception problem at their end? We've been doing these fortnightly calls for many years now, and this is a new problem. Any ideas welcome.

[Re-Titled by Moderator]

Original Title: Video problems with FaceTime