This question is for someone who has a regular arrangement (once a month, etc) with a provider.  I was wondering if you get a special deal once you become a regular client and whether most providers open to such an arrangement?

I've provided arrangements like that, but it's in exchange for convenience- usually a set day ( say Tuesdays, off-peak hours) every time. No last-minute cancellations.  

If it were more like 2x a month or once a week every month, zero cancellations, never late, always prescheduled the same day/time every time. That would make scheduling that much easier.  

I have to say that from my experience, expectations and shades of gray lead to problems in the hobbying world. I find that the beauty of a no strings attached relationship means clear financial and emotional boundaries. When one or both parties leave the black and white zone, it can cause some issues. I don't think there is anything wrong with an arrangement,  but only so long as everything is clear and discussed upfront. Proper communication is paramount.

A monthly arrangement implies a discount.  

she said she wasn't taking new clients.