As the proverb says, a chain is only as strong as its weakest link. If any of the certificates along the chain from a website go bad, it's no longer possible to verify the site's certificate. This doesn't happen very often, but it can. Even root certificates can stop being valid.
All SSL certificates have expiration dates. A CA can cease operations or stop issuing certificates. They usually give ample advance warning, but not everyone keeps up. When their certificates expire and aren't renewed, all the certificates signed with them become invalid.
This doesn't mean they'll stop working everywhere at once. Not all software is equally strict. Each client has its own set of root certificates. When the trust chain breaks, some clients may continue to accept the certificate while others reject it.
Modern browsers don't generally check the full chain. If they know that the first signing certificate is valid, they'll continue to trust it. This saves a lot of interaction with servers. Some users, though, will be affected and see browser warnings. This can be a confusing situation to diagnose. Quttera ThreatSign
checks certificates thoroughly so that you know which ones have become invalid before your customers complain.