1. Hold the Windows Key and press “R” to bring up the Windows Run dialog.
  2. Type “gpedit.msc“, then press “Enter“.
  3. Select “Local Computer Policy” > “Computer Configuration” > “Administrative Templates” > “System” >”Credentials Delegation“.
  4. Double-click the policy “Allow Delegating Default Credentials with NTLM-only Server Authentication“.
  5. Set the policy to “Enabled”.
  6. Select the “Show…” button.
  7. Type “TERMSRV/*” in the “Add servers to the list” box.
  8. Click “OK“, then “OK” again.
  9. Repeat steps 4 through 8 for the following policies:
    • Allow Delegating Default Credentials
    • Allow Delegating Saved Credentials with NTLM-only Server Authentication
    • Allow Delegating Saved Credentials

Once these policies have been set, the username and password should now save in RDP.
Delete credentials from Credential Manager, reboot, and you should be prompted to save the credentials. 

Original Site: https://www.technipages.com/remote-desktop-wont-save-username-and-password
Original Site: https://answers.microsoft.com/en-us/windows/forum/windows_10-other_settings/microsoft-windows-10-may-2018-update-caused-remote/b6324353-d21e-40f9-bbf7-75627b80355e?auth=1