This has been driving me insane for a long time now. The problem was with both 2012 and 2013.
I have NIS installed on 5 different PCs with my licence and on 4 no problems but on one for now a long time the tray disappearing icon problem plus auto live updated not running.
My educated guess is that when it tried to run auto live update it could not and then the icon disappeard. If you did run live update then manually the icon magically reappeard then you tried a second time and live update did run and complete.
Do not ask me how I came to the idea, serendipity I guess.... but I got this itch to check Windows Defender from the Control Panel (I use Win7 Home Premium by the way). And I found out that on the 4 machines without problems it was off as it should BUT on the machine with the problem was not. Or was not completely. Instead of showing me the dialog where it said it was off it opened the Defender Panel with a message like the service was not running. So I turned it on and then off. Now is off like the other cases.
Now the icon does not disappear anymore and auto-Live update runs this for over two days. So fingers crossed.