We had a similar issue with 100 CentOS 5 and Fedora 7 desktops mounting their $HOME directories from a Centos 4 server. We would see a steady (perfectly linear) increase of getattr and lookup requests from the time users logged in until they shutoff their machines (logging off stopped the linear growth but didn't always bring the number of requests down). Running hundreds of dstats and straces finally showed that the gamin package on each of the clients was causing all of the requests and simply killing that single process would instantly drop the getattr requests from 200 a second down to 3 or 4 a second where it should be. That was 200 per client so you can imagine how bad it would get! We rebuilt the gamin-0.1.9-5.rpm package and deployed it to all of the machines. We instantly saw improvement and we currently average 3 getattr requests a second. I don't know if this will help your situation but maybe someone will benefit.
Intriguing. Chris, did you have this problem with all architectures? Did you apply any patches when rebuilding gamin?