About 2 months ago I replaced the single handled shower faucet cartridge. The faucet is leaking again. Is it possible that my kids are doing something when they shower that is damaging the cartridge? Does not turning off the shower at the tub faucet before turning off the water cause damage to the cartridge? The handle pulls out to turn on the water. It turn left for hot and right for cold. If they were to slap the handle closed, would that damage the cartridge? we don't have hard water and When I replaced the cartridge, there wasn't any gunk in there. The cartridge was pre-lubricated.
I would be looking at the valve plates to see if there is scoring from the original failure. If some damage was on the plate then a new set of seals may work at first but fail as the scoring wears them down. In addition if you find rust scale fine rocks or lime build up in your airators on your faucets it could have been a chunk that was still in the valve when you replaced the last one, I usually try to flush out the plumbing when repairing a washerless for this reason. So could it be the kids sure but I doubt it.
As a parent, I can say that the answer to "Is it possible that my kids are misusing something and causing it to fail?" is always yes. I wouldn't assume it's their fault, but it wouldn't hurt to give them some kind instructions.
They can do whatever they want with the diverter valve (the valve in the tub faucet) and it won't affect the cartridge.
If they don't turn the water off all the way after showering, leaving a very slight drip, that could allow minerals to accumulate in the cartridge and prevent it from sealing completely in the future. However, it would take many days in this state before anything bad happens. And you say you don't have hard water. So, I bet that's not what's going on.
Maybe they're damaging the cartridge by the way they use the valve handle. Things to avoid include hanging on the handle or turning it too forcefully. But, unless they're really abusive, I wouldn't expect it to break in just a couple of months.
My bet is that the new cartridge either isn't a perfect fit, has come loose, or it's defective.