I'm remaking some code for a survey-system I'm the maintainer of. And one of the problems is adding reminders for the survey invites.
I made this: http://www.codepen.io/cwattengard/pen/HCrvx
I have adapted it slightly for the codepen since the original has some prefilled data coming from an ASP-codeblock. But for the codepen demo I've prefilled only one reminder (as you must have atleast one). I'm not sure if this solution is quite good UX though.
Some more metadata: There is a maximum of 5 reminders. You can only delete the last reminder at every point in time. You can not delete the first reminder (since it's compulsory).