From: ubby
I am using a windows azure one. I also tried thomas host. It had like 2GB ram and 6 cores and still had problems so I asked for a refund. The windows azure is 3.5GB ram and 2 cores
I had the same issue with Azure as well. As a matter of fact I couldn't even minimize it, it would stop working then as well. I was using Remote Desktop, but I've also tried VNC, and so far Teamviewer is the best. You may have better luck with Teamviewer, it has a specific button for "lock on session end" so maybe it won't shut down when you either close it, or minimize it.
Hope you get it worked out because it's a pain in the ass having that window open 24/7.