I agree that it's unprofessional not to reply to an email, however, I also think that it's human to get distracted and not realize you didn't do something.

Traditionally what I have done in any situation in which I haven't received an acknowledgment is to follow up.

I usually write something like, "Hello! I just wanted to let you know X. I didn't hear from you and am following up to make sure you got my initial email. If you could let me know that you did, I would greatly appreciate it! Thank you, Me"

X would be whatever - in this case "I have the emergency handled" or "everything has worked out fine!" or "Things are stable."

That way I a) provide a follow up (saving an email or two) and b) clearly state that I am expecting a reply.

And also a follow up email saves one a lot of angst as to why they didn't receive a reply.