If you read their pledge you will find the answer:
"What happens if I stop paying?
Permanent URLs are a powerful idea, and it's a feature of using Posthaven we think you should get even if you stop paying. We'll keep the site online, but you won't be able to edit content or add to it. If you want to renew, start paying again and your account will be restored.
When will something qualify for permanent storage? Let's keep it simple initially: If you pay for a year's worth of service, your content is safe and we'll keep it online."
"What happens if I stop paying?
Permanent URLs are a powerful idea, and it's a feature of using Posthaven we think you should get even if you stop paying. We'll keep the site online, but you won't be able to edit content or add to it. If you want to renew, start paying again and your account will be restored.
When will something qualify for permanent storage? Let's keep it simple initially: If you pay for a year's worth of service, your content is safe and we'll keep it online."