RDP has a few inherent issues, such as security layers, clipboard interaction, etc. The biggest one though, is that disconnecting from an RDP session will leave the system locked in such a way that Login Agent won't be able to function properly. This is a known issue.
Rather than changing your infra setup, try just changing how you access the machines. Look into something like TeamViewer, or VNC. Between the two, we've had a significantly better experience with TeamViewer.