Jeff,
I have encountered the same situation with the Project
Center. For some reason you can not add filters to the
design of the view from Admin / Views the way you can for
resources. And you are correct that filters in the view
itself are not saved.
We have used 2 different approaches to work around the
situation: one by using Groupings in the view and the
other by changing the owner of completed projects.
Groupings - although filters are not saved in the Project
Center, groupings are saved. If you group on your code
field, then all of your Active projects are already
grouped together and you would just close the other groups.
Change Owner - for all of our completed projects, we
change the owner to a fictitious project manager
named "Archive". Then in the Project Center we group on
Owner.
In either case, I have not been able to prefilter the
projects out of the view, just find ways to better manage
them being included.
Hope this gives you some ideas, Jim