if you want to keep it the same setup:
open a web browser and goto gmail.com , login, and choose 'Settings' (upper right corner) then choose 'Forwarding and POP/IMAP' and next to POP DOWNLOAD, item 2 select: 'Keep Gmails copy in the inbox' then click save changes.
if you want more consistent operation i would change your desktop mail to use IMAP just like your iphone does. to make the transition easy simply create a new account on your desktop mail client and setup the gmail as IMAP that way you can move over any emails you might be saving etc in the POP account setup.
here is the gmail guide for setting up common mail apps:
http://mail.google.com/support/bin/topic.py?hl=en&topic=12806
be well