When you work with SSDT comparison tools like Data or Schema comparison, you might enter many connections to databases. So your list of connections looks like as shown on the picture below. But there’s no button to delete unnecessary connections.
I saw an advice to choose a connection, click Edit and change to any already existing connection. Visual Studio will store only one of them, thus the unnecessary connection will be deleted. Fine! But Visual Studio needs to open this connections before you can edit it, If the connection is unavailable, so VS won’t open it.
There’s a more radical method via Windows registry. Open the branch HKEY_CURRENT_USER\Software\Microsoft\VisualStudio\12.0\SSDT\ConnectionMruList and delete ConnectionN and ConnectionNameN records there.