No network drives on the XP machine. I redesigned my program a little and now things work fine. There's really no reason for my program to first create the 8,500 files and then zip them up. My program now does the following:
(1) Create a file (and the file is not written to disk).
(2) Write the file to the zip output stream.
(3) Repeat step (1) and (2) until all the files are processed.
Thank you all for your help.