First make sure your freezer doesn't have a "fast freeze" setting, or an "always on" setting. Those are used on some units to help quickly freeze large quantities of items. Even with a partially unsealed seal it shouldn't be running all the time. It sounds as if the thermostat is bad, and forcing the unit to constantly run.
Dies this mean it is no good and too old because it is a frigidaire which isn't made in New Zealand any more. The rest of the seal is fine.
