I have a machine that may be disconnected from the Internet for up to a week at a time. It's attached to two projects - World Community Grid for the CPU, GPUGRID.net for the GPU. I have configured both projects to cache 7 days of work. World Community Grid complies gladly, but I still only get 1 work unit from GPUGRID.net.

What could I be doing wrong?

You've done nothing wrong.
There is a limit of 2 workunits per GPU here at GPUGrid.
The deadline for GPUGrid workunits is 5 days, but there is a fast return bonus of 50% for completing a workunit under 24 hours, and 25% bonus for completing under 48 hours.
There is no point in crunching GPUGrid workunits on a host which has internet connection once a week.

Alright. Thank you for that clarification.