Billing question

I was informed that if I set up auto pay I would get a $10.00 reduction in my bill. I set it up and after 2 months I did not think I was getting the reduction so I stopped it. Then before my next bill I realized that the bill had increased $10.00 a month so I was getting a bill in the same amount I was previously paying which was a reduction of $10.00. So before my next bill I set up the auto pay again and now, so far it looks like the $10.00 reduction is gone. Is this a one time thing and if you change banks or something do you loose the $10.00 benefit? Doesn't seem fair. I was not informed that the bill would increase or by how much.