Hi Daniel,
Ebay auctions are listed by closing date. So if your auction ends after your competitor, his will be first.
That is, unless you pay for a 'Featured Plus!' listing then your auction should come up in that category on top - I'm not sure if that's the case when searching for your 'keywords'.
Can you tell us what your ebay ID is? Maybe I can give you a few more ideas that would help.
-Dave
http://www.infoproductlab.com
The BEST Book on ebaY I Ever Wrote- FREE