I'm running SkyDemon on an iPad 3 and use the inflight logging feature on all trips. Sometimes, when I look at the log after a flight, I will get a message saying that there are gaps in the recording and that the actual track has been replaced by straight lines. I suspect this has something to do with the fact that I close the cover on the iPad from time to time during the flight. This of course shuts off the screen. My question is this; will closing o the lid also stop the iPad from logging the trip or does SkyDemon still run in the background?

Apps cannot run in the background when you shut the cover; I think this is probably what is responsible for the gaps in logging that you are seeing.

Well, the other app I use while flying, GPS HD from MotionX, surely does. I use it to log flights and the recorder runs with the cover closed and the iPad is in "sleep" mode. Also, in the ForeFlight app, there is an option on the Settings menu to let the iPad run in the background while the iPad sleeps. Would it be possible to have SkyDemon do the same?

SkyDemon certainly has the "continue to receive location updates while in the background" flag set like those other apps will. I thought that apps were always slept when the cover was closed, but if those other apps continue to log then I am wrong about that and SkyDemon should too. It's a very simple matter of a 10 minute car journey to test once and for all!