You will get this error if you map a custom Aha! field to the field in Jira that is not supported. This is because it cannot be set through the Jira REST API (which is what Aha! is using).
Any fields in Jira that cannot be set by the Jira REST API will not be mapped through Aha! even though they may show up on the list of custom fields available for mapping.
A common example occurs when attempting to map a custom field in Aha! to the Jira sprint field. The sprint field is key to the operation of Jira. Changing the sprint affects a number of things. The Jira UI is able to display the sprint in a friendly way, but the API does not support translating the internal representation into a form that is useful to external systems. Unfortunately, this means that Aha! (and other external systems) cannot integrate.