This has been happening for a couple of years. I don't have a Gold account, but I would stream movies from my media server through the Xbox. It worked fine for one Xbox that was hard connected to the router, but for the wireless Xbox, I would randomly be signed out of Xbox Live, and the movie would stop. Considering the Live account isn't connected to network sharing, it seemed ***, but it is what it is.
Once internet apps were unlocked without a Gold membership, I began using NetFlix as well. The problem persisted. And it only happens while watching movies. The Xbox can sit for days and stay connected to Live. Once I start watching videos, it disconnects. This is also stupid, since the NetFlix account is in no way associated with my Live account. It's even a different email. What *** me off the most is that 80% of the time, when I back out of NetFlix, I'm automatically reconnected with Xbox Live before my home screen even shows. The other 20%, I have to sign out, then back in. Most of the time the connection is immediate; on occasion, I have to "troubleshoot" the network, just to find that everything is gravy. Then it reconnects without a problem.
It's frustrating that this issue has persisted for so many years and a fix hasn't been made yet. It also explains why Microsoft is the first thing I remove on any new computer purchase, and why Xbox One won't be my next console. I've done limited research on the problem and see that it's a common issue, and in many cases, no fix is ever found. Sure, I can redesign my network and hardwire both consoles to my router, but wtf is the point of having a wireless card if the solution to all network issues is to hardwire the console.
Hopefully you smart folk will develop a fix for it, but I'm sure the "ideal" solution is for everyone to buy the Xbox One. I, like many others, will simply change consoles to Play Station. Not all of us are hardcore gamers, and even among those that are, brand support only goes as far as customer support. I know Play Station offers more all around support than Xbox, and using the console as a media device is something done by almost all of us. Sony has you beat in that category, and this light rant may ping the developers to fix that gap. Don't know, don't care, I'm just tired of having constant issues with a device that costs as much as a computer, but can barely perform it's main function (I have experienced lag issues without online play) and poorly performs even the most basic of auxiliary tasks.