Stay on as this will still hold your IP address. The only down side to this router is that you have to 'reboot' the router when you make changes, thus you might get a new IP ( I have had this problem several times).
My next question to you is, why do you shutdown your systems. They don't absorb much power and you could be using your unused CPU cycles for one of Team AnandTech's projects. (Shameless Plug). =)
Jay
P.S. Follow the link in my sig if you are interested in learning more about Distributed Computing.