When to replace the hitch pin?

x2 on everything opnspaces said.

I not only keep an extra hitch pin, but a few extra clips as I find they walk off on occasion...and it's NEVER my fault. ;)

If the pin is smooth and undamaged I would leave it alone. I would replace it if it's showing signs of damage like maybe the receiver tube gouging into the surface of the pin.

A few weeks ago I noticed that a replacement pin for a 2 inch receiver is a whole $3 on Amazon. At that price I ordered a few extras since I have multiple hitches at home. I also keep an extra in the center console of the Suburban as a just in case.
Amazon

Not a pin but I once had a ball shear off where the rounded part starts. The lower part was still in place. This happened at 70 mph on I-40 the Friday evening before the 4th of July. Thanks to safety chains and a big enough truck damage was minimal. But what a traffic mess. I guess a pin could fail.

When was the last time you have seen someone break a pin?

Safety chains are the back up for those pesky pins.
I only replace them when I have no idea where I put it. For years now I have put it back in the receiver when finished towing.

Do you really think that little pin has that much force on it towing a trailer?
I think there is a lot of friction with the TW pushing down causing the 2 square tubes to bind together. And if the ball mount is not removed often, rust will lock them together. I pull my ballmount whenever I unhook. Pin in hand, I'm certain I would notice before it failed under load. Bet most wear on the pin is when trailer is not hooked up.
Now I do keep both the pin, and the safety pin that holds it in place in my "in case" tool box. Don't expect to break, but I have lost a few.