Mr. 3000, if you wait until the guy's putting guys all over the bases, you've waited too long. There are usually signs in advance of that, and if you pull the kid based on the signs you can both save his arm and the game, quite often.
Inconsistency with the curve is one sign. If it was sharp, then it goes to sometimes sharp/sometimes hanging, that's a sign. As another indicator, I especially watch the strike/ball ratio from inning to inning. If a guy throwing 2/1 strikes to balls suddenly has a 50/50 inning, he is losing it and you send him out again at your peril.
I see coaches send kids out there again after innings like that all the time. The typical result is that the next inning is one with a high pitch count and you're lucky if you escape without runs. Better to pull him while he's still only moderately fatigued, leave the outing as a positive experience and again, save your team the runs.