I also get this error, but I can't resolve it by restarting SSMS.
If I am connected to one server (I am sysadmin on this server) I have no problems, if I am connected to another server, I get the error: "Failed to register database". I am db_owner on the database, but only dbcreator and public on this server.
the second server:
Microsoft SQL Server Enterprise Edition (64-bit)
What rights I need on the server?