I don't think you have much recourse, but I agree that being notified at 6:04 p.m. for something that had a 2 p.m. deadline is a pretty clear-cut case of getting screwed. Yes, you technically could have mitigated it by checking the app, but the fine print doesn't say "We will notify you via email, but email delivery times are inherently unreliable, so you should probably just check the app exactly at 12 p.m." It just says you will be notified via email.
No idea why people are attacking you instead of just being sympathetic. Winning the lotto but getting the email too late to claim it definitely sucks.
ItsMeRaul said: "The production bears absolutely no responsibility as to if/when email is received."
You have absolutely no idea why the email showed up late, so you can't really claim to know who or what is responsible. For all we know, the production's email server could have bugged out and sent the email late.