I'm not sure fixed IP-s are a must (eg I have a normal DHCP address on my aTV but reserved address on iTunes server), but proper DNS service and iTunes Store access are vital for Home Sharing authentication.
Don't know if it plays a role, but I use a separate Apple ID for Home Sharing purpose only. All the Macs and iDevices in my household Home Share with that ID. Everyone uses his/her own Apple ID for Store purchases & downloads.