Remote Desktop fails after VPN connection

Are you using the same IP address for the VPN and the remote desktop? If not, are you using the default gateway on the remote network? If so, does the remote router support NAT loopback? If not, then your packets won't be routeable after you establish the VPN.

EDIT: Sorry, I misunderstood the question.

If your VPN is set up to use the default gateway on the remote network, then you will normally need to VPN to the remote network yourself and re-establish the remote desktop. But you can work around this by adding a static route back to you from the remote PC which should override the VPN default route.

For instance, if your public IP address is 1.2.3.4 and the remote desktop's default gateway is 5.6.7.8 then you would use

route add 1.2.3.4 gateway 5.6.7.8

Then when you connect the VPN the remote desktop still knows how to route packets back to you.

You really are not giving a lot of information. You should put things like networks (192.168.1.x, for example), and what VPN client you are using.

If you are using the Microsoft VPN client, I would try just unchecking the box: "Use default gateway on remote network" as in the image: