There is no question about it, Skype has had some serious issues with reliability recently but the company is actively working to fix these issues and now we are starting to see the fruits of their labor.
Microsoft has informed me that they have released an update that addresses the issue where a web-instance of Skype would ring continuously even if a call was answered on another device. In addition to stopping the ringing, this should also help address the issue where messages would show up out of order as well; although it may not totally eradicate the problem.
To test out that the bug is truly fixed, Paul and I attempted to recreate the scenario that would previously cause the issue. Both of us opened multiple browser sessions of Skype, logged in with our phones and of course the desktop client too; when we called each other (he called me, then I called him), the ringing stopped once it was the call was answered, amazing...
Read more: Microsoft Fixes One Of Skype's Annoying Bugs, Continuous Ringing - Thurrott.com