Remote desktop disappears after login

A couple of thoughts:

• Has the target machine out of resources? (Do you know anyone who can have a look at the physical desktop?)
• Has the target machine out of remote connection licences (or whatever the limiting factor is)? I'd have expected a decent error message in that case, admittedly.

Is there anything useful in the event log on either machine?

Like you wrote in your question, I think the driver of the graphics card is the culprit - I mean the driver of the computer where the Remote Desktop client runs.

Even if you haven't changed anything in the video configuration, there may be something new (software, icons, anything...) on the remote machine which causes the video driver to go crazy.