AppleTV Air Mirroring: does the signal go through the WIFI router

If you consider a movie to be changing data 24 frames per second and compare the size of the menu art compared to the size of a movie screen you will quickly realize the menu items are negligible.

You will blow through a months worth of menu data in less than 4 minutes of a TV show through netflix or one short youtube video.

Do watch your data consumption - streaming music is moderate use - streaming video is heavy use.

I've had this experience with my wife's MBA and discovered our wifi channel was to close to other access points in the neighborhood. You would think this nearby interference would cause connection problems throughout the day but it actually occurred just like you've described. Ok for hours than down hard.

I changed the channel on our access point away from the nearby channels and the problem went away completely.

You can use an app like iStumbler to view available networks and what channels they are using. To view the wifi connection for your MBA, hold down the Option key and click on the wifi icon in the menu bar.