Every SSL certificate has an expiration date. Now suppose some site's certificate expired an hour ago or a day ago. All the software by default will either just refuse to connect to the site or issue security warnings.

This recently happened to Windows Azure Storage and since most of software in dependent services defaulted to refusing to connect lots of services experienced major degradation.

Now what's the logic in here? I mean a day ago the certificate was valid and everyone was happy to use it. Now a day later it's formally expired and noone likes it anymore.

I've read this answer and I don't find it convincing for this specific edge case. To every security model there is a threat model.

What's the threat model here? What could have happened between now and a day ago that a certificate is treated to be unusable to such extent that we even refuse to connect to the site?

When a certificate is expired, its revocation status is no longer published. That is, the certificate might have been revoked long ago, but it will no longer be included in the CRL. Certificate expiration date is the cut-off date for CRL inclusion. That's the official reason why certificates expire: to keep CRL size bounded.

(The unofficial reason is to make certificate owners pay an annual fee.)

So you cannot trust an expired certificate because you cannot check its revocation status. It might have been revoked months ago, and you would not know it.
