2 Answers

I found this on the Skype community forums 

The easiest way is to:

1. Open the video in Google Chrome. Enter the Code (in one of the most dramatic prompts know to man, "it is time") and click play.


2. Once the video is well underway in playing, press F12 to bring up the Developer pane. Under "Frames" click on the header with a jumble of letters and numbers, then scroll down to XHR.


3. Right click the "flvs-play" resource reference, then either "Open link in new tab" or "Copy link location".


4. Press CTRL+S then save that file to whatever name you want. Before clicking OK, add the suffix ".flv" ("add that to the end of the name" is what I am trying to say). 

You now have a usable file. Hooray. The other methods still work, this is simply MUCH EASIER. 

http://community.skype.com/t5/Windows-desktop-client/Download-a-video-message/td-p/1440237

As far as I know when you leave a message it is not possible to save it as is.