While I understand the desire to never delete a feature or story either in Aha or the integration partner (Jira in my case). I would like to see a feature that flags the deleted item in Aha as being removed. This would allow me to manually review and cleanup or even report on it based on that flag.
I have exactly the same request with Rally integration we are using.
I understand Aha features auto deletion might not be desirable to prevent data loss from happening but not having any suppression notification from the "Integration update" panel or directly from within the Aha item itself is painful : we have regularly "zombie" features in the Aha dashboards coming from the Rally suppressions that are difficult to identify...