Responses
Depends on when they die. A lot of these stories have the issue of having them live until 21. So at a certain point they WILL learn what happens. Now if they always die at 16 years old or less, then yes. They'll be stuck as a child, however if they die as even a young adult they'll grow.
Thinking about it they'd probably learn by the 3rd life, if one of those lives goes well. It all depends on how much of the adult world they're exposed to.
For fools:
Even if a child repeat life for enternaty they won't become adult, they are kids who deserve to be loved and protected.