Is there anything on your system that might be creating a virtual network adapter or making another hardware change? That seems to get a lot of people who experience the issue of losing access periodically. It could be some type of virtual machine, or in my case my Motorola phone.
When I plug my phone in to my computer to charge it the driver creates a network adapter used for tethering so that if I wanted to, I could use its data connection as an Internet connection. Steam sharing looks for certain hardware changes and if it finds one, determines that the computer is different, or different enough, from the one that your friend authorized and won't let you share. It would then throw an error if I tried to reauthorize using an already installed game.
It drove me nuts for awhile. All I need to do is make sure that my phone is unplugged when Steam starts up. I can then plug it in and sharing works fine.
