They don't die, it just robs them of their stengtht. So if you happen upon one and he wants to eat you, which they appear to enjoy doing, bow to him. Kappas being polite will bow back and all the water will spill out.
Sure, he wants to kill and eat you, but at least he's polite about it. That's the trouble with society nowadays - nobody takes time for the little things.
Kappas have water on their head, yes- myths vary if it kills them or robs them of their strength, but it's always water from their sacred pond (sacred to them, at least). It stays in with magic while it moves, but if pushed over (or in some other way someone tilts his head) it can spill out.