Email notifications are not being sent when the submission is edited.

Our email notifications do not seem to be going out on post and updates.

I am not sure if I have understood your question correctly. Do you mean to say that when your submission is edited/updated, submission emails are not being sent?

I did check your form's notification email alert and you have already enabled "Send on Edit" setting which will send the submission emails after the submission is edited. I also checked our email logs and found that submission emails on edit is being sent successfully. Please check the screenshot below:

Are you receiving the initial submission emails correctly? Have you checked your SPAM folder already? Please check your SPAM folder and see if the emails ended up there.