When you delete a hosted zone and then put it back, you're not exactly putting it back. You're just creating one similar to (but not identical to) the original.
So don't do that. But, since you already did, here's the fix:
When you click on a domain in "Hosted Zones," you see 4 name servers assigned to the hosted zone by Route 53 on the far right side of the screen.
Each time you create a hosted zone, these 4 values will almost always be different -- meaning that your hosted zone now lives on 4 new, different authoritative name servers in Route 53 than the ones it was previously deployed on, when you were using the old hosted zone.
But the Internet is still expecting the old 4 nameservers to have your records... which they don't, because you deleted the original hosted zone.
You have to update the authoritative nameservers with your domain registrar. In this case, that's actually a different part of Route 53.
In the Route 53 console, click "Registered Domains."
Select your domain.
Choose "add/edit name servers."
Enter the correct values for the Route 53 name servers, which are the ones mentioned above, which you'll see when you click on the domain from the Hosted Zones page.
Most of this content is from my answer to a similar qestion at Server Fault.
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