If a renewal charge fails, Stripe retries the card over the following days and emails you a link to update your payment method. During this time your subscription shows as past due; your links keep working while retries continue.
If payment ultimately cannot be collected, the subscription is cancelled and your account drops to the free tier, which pauses your links until you resubscribe.
To fix a failing card at any point: Billing, then Manage subscription, then update the payment method.