Dewight, I have only had FTM for a week. I noticed the same thing when I downloaded my tree from Ancestry to FTM. I made sure I stayed signed on overnight and left it there working (I shut off the monitor)
That was last Friday. Best I can figure it is always working if you have internet access and have your FTM set for work online. I don't find it causes any problems but here is how I found to stop it.
Open your FTM. Click the file button on the left side of the screen and go down to "Go Offline". It is just above the exit button.
Now look at your FTM and you should see it no longer says it's adding media in the background. Keep in mind it will turn on again the moment you click the search the web button while in the program.
Mine has stopped a couple times on it's own and started up again. I think that is normal or maybe Ancestry was having issues or my internet access was. Don't fix what isn't broke. There are enough potentially serious glitches in FTM. I don't think this is one.