That did not allow me to create Local computer credentials. It has now been almost three weeks since I first looked at all of this, and nothing allowed me to create Local computer credentials.
But the big question is this: what, very specifically, changed from Windows 7 to Windows 10? As I noted, I had been using the same saved credentials for some years, and two days after upgrading to Windows 10, Windows began deleting the credentials intermittently. For sure, the credentials are deleted if I lose my connection. I have a somewhat unstable DSL home/office connection, and perhaps once every day or two, I lost all my RD connections. Upon reconnect to at least a couple of the servers, I am prompted--with no option to save password--for the Remote Desktop Gateway username & password.
So I have no proof that this is even about persistence. It just seems that nobody--Microsoft included--understands what they have done to Windows in this regard. For the record, I have many clients that have the same problem; I set them up to work remotely, and they are prompted for RD Gateway credentials (but not the remote computer--those credentials are correctly saved) at each logon.
I seem to have to do something like this: after being prompted for RD Gateway credentials, enter them and log in. While logged in, go to the Credential Manager and manually add a Generic credential. It seems inconsistent, though.
Here should be a big clue: when I go to Advanced → Settings and click "delete" to delete the RD Gateway credentials, nothing happens. It used to immediately switch to user name "None specified" and offer the option to "use my RD Gateway credentials for the remote computer". But now it just keeps the logon settings. That has got to be some sort of bug. In fact, when I deleted the credential for one of my clients' RDG servers, the screen did not change, but when I then tried to connect, it brought up as a suggestion the username from a different client's RD Gateway server.
So I need specific information on exactly where in the registry or system this information is stored.