There are a whole lot of restrictions like this, because the society there is so small and isolated it basically doesn't have the infrastructure to deal with childbirth, very sick people and old people. But people who live there and have babies on the mainland do bring them back to Svalbard after they are born, and there is a kindergarten and a school. You're allowed to stay there after you are retired, but then you're on your own, you can't ask for any of the healthcare benefits that pensioners are entitled to.

There's also a whole lot of other exceptions, like different taxation from the mainland, exemption from needing a snowmobile licence to drive a snowmobile, permission to carry firearms almost everywhere, etc. The prices of e.g. milk and fresh produce are astronomical, while alcohol is cheap.