After much search, and questioning, I discovered that I need to delete the Geoprocessing object, then re-create it as such:
import arcgisscripting
from time import strftime
print str(strftime("%H:%M:%S"))
gp = arcgisscripting.create(9.3)
gp.overwriteoutput = True
print str(strftime("%H:%M:%S"))
del gp
print str(strftime("%H:%M:%S"))
gp = arcgisscripting.create(9.3)
gp.overwriteoutput = True
print str(strftime("%H:%M:%S"))
I did it twice, and measured the time. The first time you create the object, it will take the longest. On my machine, it takes 3 seconds to initialize, but after that, the process takes less than a second. Since the processes I am running already take 2-3 hours to complete a 1-2 minute increase is not too hard to live with.
I found that if I delete the geoprocessing object after I perform work on about 3 processes, I eliminate the error.
Enjoy