This has been a talked about feature in the forums for a while and now with the advent of Zapier I think there's no better time to implement it. The push notification would be for when a customer is a certain amount of time away from their membership expiring. This would allow us to much more accurately avoid churn by sending certain notifications.
Thank you for this suggestion! This feature request or some aspect of the functionality suggested is currently being reviewed for possible inclusion in a future update. If there is additional information, this post will be updated to reflect it.