I don't know how it is now but in the past the ethermine dead miner alert email always arrived late.

If you want something more instant just use the Claymore manager and add your email there. You will need some POP3 mail server and its a pain to figure out at first but its the best way to get alerts instantely if any of your rigs go down.

However keep in mind it won't work if at your location your internet is down, if its down then there is not much you can do either way. You can't mine without an internet connection anyways.