I wonder whether a new, simple SharePoint list mapping would work. Would you be willing to step thru a very simple form mapping to a very simple list, and verify whether that works correctly? This would at least tell us whether it is an issue with the environment or the form.
A. If your simple (new) form and new mapping work, then it's an issue within the current form itself.
B. If your simple new form and mapping fail, then we can guess it's an issue in the environment.
Would you mind doing this as a troubleshooting step? Create a blank new form, inject it with qRules, create a ShP list, and then create a mapping between the form and the list. Publish the form and test it out. Let us know what you find. Thanks!