Pretty strange, all right. If you open the Windows Task Manager, can you tell if it is running? There should be an entry for "Python", which should look something like the attached image. If you see it, Leo is running but somehow invisible. If not, Leo has quit. Also, is it possible that there is a Leo icon in the task bar, even if Leo itself is invisible?
You could try the Event Viewer. Open it, and look in Windows Logs/Application. Filter the view to show only errors, or errors and warnings. With luck, there will be an entry for you, and with more luck it might even say something useful.