What the receiver actually checks
Behind this message sits a three-step check known as forward-confirmed reverse DNS (FCrDNS):
If step 1 already fails you get “cannot find your hostname”. If step 2 fails, Postfix says “cannot find your reverse hostname” — the PTR exists but points to a name that does not resolve back to the same IP.
Why this is temporary
The 4 class is deliberate: DNS outages pass, and a receiver does not want to discard mail permanently just because a zone is briefly unreachable. In practice this means you have time — the sending side typically retries for several days. Set the PTR within that window and the mail goes through on the next attempt.
Who sets the record
The PTR is not managed by your DNS provider but by whoever owns the IP block — your host or ISP. On servers with a dedicated IP it is usually in the customer panel under “Reverse DNS” or “rDNS”. Without a dedicated IP, for instance behind shared NAT, no suitable PTR can be set; the route then goes through a provider smarthost or relay.
One thing to watch: one PTR per IP. Multiple PTR records on the same address are treated as invalid by many receivers.