It is really annoying that the remote desktop client sometimes remembers only your login name but not your password, because:
Your credentials did not work
Your system administrator does not allow the use of saved credentials to log on to the remote computer COMPUTER because its identity is not fully verified. Please enter new credentials.
To fix this start the Local Group Policy Editor (gpedit.msc), and navigate to this branch: Computer Configuration –> Administrative Templates –> System –> Credentials Delegation. Here open the Allow delegating saved credentials with NTLM-only server authentication option and set it to Enabled.
Click the Show… button in the Add servers to the list option and add the servers you want to apply this setting to. You must use the TERMSRV/computername format to specify a single computer, or you can use TERMSRV/* to refer to all servers.