Yeah, the Dutch originally "purchased" the land from the Natives, in typical colonial fashion. During the second war, which was launched by the English, they were attempting to unify their colonial holdings. So they seized New Amsterdam and Fort Orange, which were logistically important locations. But they didn't seize all Dutch holdings, which allowed the fleet to counterattack in the next war.
Thing is, "captured" was largely because there were only token forces there, and the colonists were not fans of the Dutch leadership, who failed to protect them from native assaults. They didn't receive much better treatment from the British at the time, either, unfortunately. It isn't too hard to understand why New York was a center of patriotism during the revolution.
And with the Dutch Empire being spread too thin, it wasn't much for them to give up their new world holdings. They were always more successful as accountants and middlemen anyway.
![Smiley: lol](//zam.zamimg.com/i/smilies/lol.gif)