Remote Desktop and VPN Issues – How to Fix Remote Desktop Disconnects When Connecting to VPN on Remote Server

Did you check the event log for hints? Is this a domain controller? If not, is the server in the same network as your domain server(s) or on a low-bandwith connection?

Or maybe there is a program starting (antivirus?) and delaying the logon process.

What's happening is that you're effectively cutting off the IP route from the server to yourself - hence the RDP session loss. You can fix it by setting up the VPN in a way that it's bound to a second interface (physical or virtual) so that both the VPN and RDP link can coexist. How you do this depends enormously on a range of very detailed configurations that we don't know right now, so if you want help with this you'll have to come back to us with a LOT more information, just as much as you can please.