I'm having this problem also, but it started a few weeks ago when I tried connecting my windows 8 laptop with my Xbox 360 using Xbox Smartglass. The connection between the devices were spotty and didn't really work, so I'm trying to redownload my profile and the app on my laptop to see if that works. It isn't my internet connection, my xbox is hardwired into my router and I never had these issues in the past year I've had this internet provider, plus my roommates xbox can use my profile and Live just fine.
What happens to me is ill get a notification Mid-game/movie/Netflix/youtube/etc. that I have been disconnected from Xbox Live. I'm immediately able to sign back in, but within an hour it happens again. It does not give me a notification that my profile was last on another console either, so being hacked isn't the problem.