I believe it has to do with the kind of session Jenkins uses to connect to the Windows agent.
I encountered a similar scenario some time ago. I cannot explain the technical implications under these choices, but I can tell you what worked for me.
Configuring jenkins as a windows service did not work for me, but running the .jar as part of a startup script did work.
I could not see what jenkins was doing on the VM when I connected via RDP. I had to use TightVNC to see it interacting via the browser.