If your palico drops below half health, they stop using the tools, and will seek cover until they can drink and heal back. Tailriders, however, fight to the death.
The secret is that since Palicos level up, unlike stupid dumb clumsy humans, their base stats go up way faster than their gear stats ever could. Optimizing the attributes of Palico gear means getting like, +40 instead of +36 on top of your base 600-something, and it ultimately just does not matter.
In my experience, the palico armor isn't really very important aside from looks, yeah. They're never going to solo a monster for you, and if they do get knocked out they don't stay down nearly as long as they did in prior games, so you can go full fashion on them without much worry.
Better (or more elementally appropriate) armor means your cat spends less time healing itself and more time attacking or using support items. It may not seem like a big difference, but there's nothing worse than when you desperately need to be woken up from stun and your cat is chugging a potion.
