As an authority on the subject, I submit that since "Damon" is pronounced Day-mun, that "daemon" must be pronounced Dee-mun, as it's just an alternate spelling of "demon".
But mostly I just want to stop being confused whenever someone says "daemon" around the office, and I think they're talking to me.
Typically in English, an e after a vowel indicates the vowel should make a hard sound rather than soft. So looking at it that way, Daemon should have a hard a (like the name of the letter), thus DAY-mon.
The guy from the Bourne Shell Identity?
See, Team America: World Police for clarification.
It really gets interesting when you work (as a sysadmin in a Unix shop) for a guy with that name.
I've never been called "demon," but people are constantly calling me "DAY-MEE-ON."