One of the ways that you can find out whether a child has magic or not, is to see whether they are able to use it subconsciously, such as by defenestrating them, and seeing if they stop themselves from being killed. But once they get their wands, that use of subconscious magic seems to stop entirely.
Logically, you would expect students to fire off similar magic when their lives were at risk, or their emotions ran particularly high. Is it a function of having the wand that stops it, or is it just a matter of that only happening for really young mages, and that they learn to control themselves as they enter childhood?
Its been a while since I’ve seen the movies, and I’ve never read the books, but here’s a wiki article that explains it a bit.
It’s basically summed up as an unpredictable instinct in young children. I’d guess that maybe that’s lost as they get older and can think more concretely. Probably adding wand foci and being drilled in using then so much in Hogwarts also diminishes that innate ability. It seems that as you become more dependent on foci, the more difficult and unpredictable wandless magic becomes.