It's an interesting idea, but I'm not so sure about your price structure. I guess that you don't want to bill for every notification, but have you thought about billing for prevented no-shows (maybe on top of a base-price that includes x appointments)? You could still make the case that your Reminder pays for itself after the first no-show and make more money off of users that benefit more from your product.
Also: I don't know who the target audience for the base-price is. If you know you have 10 and only 10 appointments per month, this plan may be fine, but otherwise? Why not change it to a "1$ for every appointment"-Plan?
What do you perceive as the benefit to my business from going from an easy to understand option to a complicated one which requires forecasting, math, complexity, and anxiety about marginal costs nagging at my users every time they sign in?
target audience for the [personal plan]
Productivity bloggers. It exists to give my business something to offer them, because they have something I want, and it is not really their money. shh
I completely see your point about the fixed rate. However, the benefit of a flexible plan is that you can lower the price of the initial payment and make a little money every time you are really helping your customers (detecting a no-show). You potentially save your customer money and take a fee for this service. I get now that that's not what you want - just wanted to offer a different perspective.
Also: I don't know who the target audience for the base-price is. If you know you have 10 and only 10 appointments per month, this plan may be fine, but otherwise? Why not change it to a "1$ for every appointment"-Plan?