Using the subscription.unpaused webhook, you can have Bizplay send a notification to your administration system when you remove a Paused at date from a subscription. You do have to make sure that the subscription's External reference in Bizplay contains the ID of the corresponding record in your administration system.
If you're not using the subscription.unpaused webhook, then you need to make sure that you remove the pause date in Bizplay as well as your administration system.