Registrars warn you that the process of moving a site (and changing nameservers to do so) can take up to 48 hours to propagate. That's one thing - but why in the process of propagation does it work one minute and not the next?
Because the other name servers in the world sync their zones on a schedule. When their timer is up, they refresh their information.
This timer is usually set to a value of several hours. Until most nameservers on the world (that care about the domain and have it cached) have refreshed their zones, you will get the old result.