To expand on Douglas_Knight's answer, if it seems counter intuitive that is because children spend basically all their waking hours in a learning environment for nearly two decades of their life. Most of that time is spent learning or using in some way one or more languages.

The typical adult method for learning a second langauge, on the other hand, is to spend an hour or two a week in a classroom or with a tutor. No wonder it doesn't work as well.

To compare apples-to-apples, consider for example the Monterey Naval Postgraduate School which trains American soldiers and intelligence officers. Using a full-immersion, 24/7 learning environment they are able to take adult learners from zero to near practical fluency in months to years (depending on the difficulty of the language). Similar results are reported with Peace Core volunteers, for example, at least those which find themselves in a fully non-English environment.

No, it doesn't depend on how you define "children." People get continually better at learning second languages, up at least to age 16. For every aspect of language (except accent) that people have measured, older people learn faster. Forget your anecdotes and read the literature.