I'm not sure from your description, but does it go this way:
You play just fine. You shoot a UFO down (or discover that one has landed). Then you send your X-Com Squad to blast those aliens. Then, after you klick OK on the briefing screen (go there, kill aliens, collect alien artifacts...) you see the desktop.
This happens to me
, and to you too, it seems. However, I discovered that the game is still running. I use XComUtil, and at least with it there is a dos prompt left running, but it is minimized. I maximize it and press some buttons in the keyboard, and usually it hops back up and lets me play the fight. I did it accidentally the first time (trying to write 'exit' on it, as I mistook it for a regular dos window), and it doesn't seem to happen if I just wait.
However, despite a slowing program (or maybe because of it) the battle's speed sometimes is WAY too high (mouse to the side of the screen = view instantly teleports to one of the corners, autofire sounds like machine gun, I can barely see the screen changing before a shot has travelled through a few screens and hit the end of the map...). I had real troubles trying to play a Terror mission that acted like that. During that mission I realized that I can center on the chosen soldier and move the center of view from the map screen.