I hit this problem today, I don't see this in any of the tips, but i suppose it could be hidden in all the questions.
On a hunch i figured this could be the most likely thing turning off the adapter are the power-management settings. It seems i am right in my case, after doing this the adapter seems to stay on.
A good thing to check if you run into this: Please go into your Device Manager\Network Adapter\Xbox Wireless Adapter for Windows\Power Management (tab). Un-check all the power management features (namely in my case Allow Computer to run off the device to save power). Note this could impact the life of your adapter since it will run more, but it seems quite useless in a state that when you are gaming it disconnects to save power.
Note to Microsoft\Xbox: given you manufacture the controller, and the operating system it might be a good idea to investigate this issue so that you don't drive customers way :) Pun intended.