I had the same issue after upgrading to Sierra.
I did what other posters suggsted "In RDP Client Preferences, go to Security and check "Always connect, even if authentication fails."
This worked. However, now an "enter your credentials" window opens every time I connect to my PC. Before the Sierra upgrade I did not have to enter my username or password each time.
The "enter your credential" window has a box for "add user information to keychain", which I have checked. I also went into RDC preferences and on the "login" tab I made sure my username and password was correct and I verified the "add user information to keychain" box was checked on that page too. I tried logging into my business portal via Safari and keychain worked to provide the login information there.
Does anyone have any ideas on how to resolve this?
Thanks!
Mark