As a Linux system administrator, I am familiar with the definition of the term "daemon" as a process running on a system, usually backgrounded, that provides some sort of service, like a web server or file store. When I first started my career, I prounounced the "ae" with the long "a" sound as "day-mon". It seems everyone I interacted with agreed with me.
Then I got a new job at a startup when my boss heard my use the term. He pulled my into his office to correct my behavior:
"Daemon" is pronounced with a long "e", similar to how you pronounce "Caesar". When you see "ae" together, it's always with a long "e". The term itself goes back to Greek mythology. The spelling is the older spelling of "demon" and they are pronounced the same.
This was around 2011. What he said resonated with me and I found other words with "ae" that had the long "e" sound, even if they were spelled archaically:
Archaeology
Caesar
Encyclopaedia
Haemoglobin
Orthopaedic
...
I was a convert. So much so that I was giving a presentation on systemd administration to other system administrators. At one point while discussing service units, I mentioned that "oh, by the way, the word spelled d-a-e-m-o-n is pronounced dee-mon, not day-mon. Think Caesar, encyclopaedia, archaeology, haemoglobin, etc." Well, one attendee in the presentation wasn't satisfied. When I finished and opened the remaining time for questions, he asked:
What do you call a dessert with bananas, ice cream, chocolate syrup, sprinkles, and a cherry?
Of course the answer is a "sundae" and the rest of the attendees got a good chuckle, as I was caught off-guard and didn't have a retort. But that got me thinking: just how many "ae" words exist in English, archaic spelling or modern, and how are they pronounced? An easy regular expression search on my Debian system returns that answer:
I get 205 results in my search; your mileage may vary. However, when I scan the results, here are some that stand out. Obviously this isn't an exhaustive list, and this is also how I would pronounce them which follows General American pronunciation. Recieved Pronunciation or other English dialects my pronounce them differently. Archaic spellings are italicized:
Long "a"
aerate
antennae
Gaelic
Praetorian
pupae
reggae
sundae
Long "e"
aeon
algae
archaeology
Caesar
encyclopaedia
haemoglobin
orthopaedic
Short "e"
aero-(bic, dynamic, nautics, sol, space)
aery
haemorrhage
Short "i"
caesarean (first "ae")
Michael
Rachael
Syllable separator
caesarean (second "ae")
Ishmael
Israel
Kafkaesque
I think it's fair to say that the pronunciation of "ae" is varied. Is there a single authoritative source we can use that settles the debate? I don't know, but I'm willing to trust Wiktionary on this one:
Etymology 1: A borrowing of Latin daemon ("tutelary deity"), from Ancient Greek δαίμων (daímōn, "dispenser, tutelary deity")
Pronunciation: IPA: /ˈdiː.mən/
Etymology 2: From Maxwell's demon; a derivation from "disk and execution monitor" is generally considered a backronym.
Pronunciation: IPA: /ˈdiːmən/, /ˈdeɪmən/
In the case of "Etymology 1", the pronunciation for our Latin deity for both Received Pronunciation and General American is strongly "dee-mon". However, is the case of "Etymology 2", our pronunciation is both "dee-mon" and "day-mon" according to IPA.
Wikipedia's article on "daemon (computing software)" agrees:
In modern usage, the word daemon is pronounced /ˈdiːmən/ DEE-mən. In the context of computer software, the original pronunciation /ˈdiːmən/ has drifted to /ˈdeɪmən/ DAY-mən for some speakers.
So, "dee-mon" or "day-mon", you're not wrong.