Two possibilities I can see:

1. They right-click the icon to remove it, usually accidentally. As a tank, I always try to remove regen before every pull and have on a couple occasions accidentally removed protect by mistake. (PSA: pls don't renew regen/whispering dawn right at the end of a kill, it makes the next pull more chaotic. There's a full GCD between the initial Shield Lob/Tomahawk and the first Flash/Overpower and a regen will cause all the additional mobs to head straight for the healer/fairy instead of the tank.)

2. They already had a stronger protect in effect on them, so the duration wasn't actually reset. You may see time remaining on your protect, but their timer was still the old protect's timer. You can notice this at the moment you cast protect in a couple ways: Target them and view their duration to confirm it has the full 29m duration, or pay attention to the flying text to see if it says 'Protect has no effect!' This only really occurs when playing as a Scholar or an untraited White Mage trying to over-write a traited White Mage's protect.