A few months back, rbox updated his pre-rooted ROM for the Fire TV 2 to disabled the stock recovery so that official Amazon over-the-air updates would not install if they managed to download onto the device. It turns out that isn’t actually the case. After an XDA member was surprised to find his rooted Fire TV 2 had updated, I did some testing and can confirm that a rooted Fire TV 2 running the latest 5.0.5_r4 pre-rooted ROM, which downloads the 5.0.5.1 update, will automatically install the update and lose both root and TWRP. It’s unknown if Amazon changed something to force the installation, or if the block rbox put in place never worked from the beginning. Regardless, as I’ve always advised, you should be blocking updates if you want to keep root and never rely on TWRP to reject a stock update.