Auto-refill pop up..how many times should this show?

I work for a healthcare company. We offer the opportunity for patients to auto-refill their prescriptions, but not everyone knows that it exists. Business wants to add a pop-up after an online order is confirmed to help enroll patients in the auto-refill program and there's a hard drive from business to have this appear every time, however we believe that would be a bad experience and want to show through testing why that would be.

Exact call to action of the pop-up is still being figured out, probably something along the lines of "Yes, enroll me" and "Not now, thanks" (with another option that you can select "Don't ask me again"). Obviously, if someone doesn't select that "Don't ask me again" but also X's out or says "Not now, thanks" more than once, it's not a good experience to continually ask them over and over if they want to enroll in auto-fill every time they order (typically every 90 days).

Is there a best practice or any research on how many times a dialog like this can be shown before it becomes way too annoying?