Since you didn't specify time period, I'll throw in for medieval/early modern Europe.

Most of the time it's just some sort of illness (often difficult to determine because of the terminology and understanding of medicine at the time). Very much of that must have been bacterial, so just as with adult deaths, many just couldn't have been prevented without our modern-day antibiotics. Certain medical treatments, like bleeding, would of course have just made the illness worse, so not doing those things would have helped in some cases.

The death roles also contain a lot of accidents: falls, lots of burns (remember all cooking is done over a fire), some drownings, animal bites. Although these are listed as the cause, in many cases the child probably succumbed to the secondary infection. So again, antibiotics.

There's an interesting project going on now, here, that's finding that children seem to have been way more unsupervised than we would expect, so that would also have contributed to accidents.