In troubleshooting another problem, I came across a suggestion to run rsop.msc on the client machine. Rsop.msc displays all the group policies that are applied to a domain machine. In my case, it helped me track down a group policy that was forcing machines on the domain to never go to sleep. I guess that policy makes sense with desktops, but a particular user did not want this behavior on his laptop.
Anyway, rsop.msc made this much easier and is a tool I'll keep in mind.