No different really than losing your handicapped parking permit. You get another one.
The silver lining here is that legit dogs and owners are pretty easy to detect without the need to see certificates. Like, with surprisingly high accuracy. No red flags, no spontaneous audit needed.
You have a (well behaved, non-geriatric) lab, a golden, various herding/working dogs, you could much more safely assume a legit dog and blow off an audit.
But you try to bring a chihuahua, pit, pug, wiener, or any non-ideal breed on a plane (or anywhere), and you're gonna get audited.
Hint: almost all of these are amazon vested, home trained, pets being declared legit because reasons.