When the problem is theirs.
HOW TO TELL
Cloudflare publishes a status page. Check it.
If a widespread incident is in progress, it will be there.
WHAT HAPPENS TO YOUR SITE
If Cloudflare is unavailable and your records are proxied, your site is unavailable, regardless of our servers being fine.
That is the trade you accept by putting a service in the path.
WHAT YOU CAN DO
Set the affected records to DNS only. Traffic then goes directly to us and the site returns.
Propagation is fast for Cloudflare-hosted DNS, so this takes effect quickly.
Set them back afterwards.
THE CAVEAT
If Cloudflare's DNS itself is affected, and your nameservers point there, changing records does not help because nobody can look them up.
That is rarer and it is the more complete dependency.
WHETHER THIS SHOULD WORRY YOU
Cloudflare is reliable, and no service is perfect. Incidents happen and are usually short.
WHAT TO HAVE READY
Knowing how to set records to DNS only, and having your zone exported.
Five minutes of preparation for an event you may never need.