Error: NOTE: Failed to notify 'operator' via email. when trying to send e-mail when job fails

As you allude to in your question, my issue was indeed the mail profile in agent - thanks for the tip.

enter image description here

Other tips that are mentioned at the bottom of this post include:

  1. Ensure DB mail is enabled within the SQL Server Surface Area Configuration. Do this by right clicking the server name and selecting FACETS from the menu Select the 'Server Configuration' from Facet dropdown Ensure Facet Property of 'DatabaseMailEnabled' is True

  2. Set up a Mail Profile within the Management Folder of your server

  3. Within SQL Server Agent set up an Operator

  4. Look in the properties of the SQL Server Agent (right-click properties) and under the Alert System page tick 'Enable mail profile' and select your default profile that you set up in step 2.

  5. Restart the SQL Server Agent


Second restart of SQL Agent fixed the problem.