Tell us about your battery. How old is it? Does it hold a charge? Have you tested it? Possibly, your battery is not accepting the charge for some reason. Are you testing the regulator and stator while under load or independently? (Back probing while increasing and decreasing rpms) with all components in circuit.
This is food for thought, but, im leaning more toward a wiring problem in the charging circuit. If the stator and regulator are new and working, the problem within the circuit should show resistance and voltage drop when back probing during operation.
Specifically, how are you determining the system is not charging during idle? These problems are difficult and even more troublesome trying to troubleshoot online. Bear with me, I know some of these questions are basic and redundant. You are the eyes and ears, we are trying to visualize what you are experiencing.
We need to know where the current is going or where it is bleeding off. Where specifically within the charging circuit.