Assuming there are open connections through an active system's NAT and a fail over occurs, by default, what happens to those connections.

This is incorrect because connection mirroring is a fundamental high availability feature that prevents connection loss during failover for stateful connections like those handled by NAT.

BIG-IP systems are designed for high availability, and by default, connection mirroring is enabled for NATs and other stateful services. This feature ensures that the standby unit receives and maintains a copy of all active connection states from the primary unit, allowing existing connections to persist seamlessly through a failover.

While mirroring is involved, it's typically enabled by default for NAT configurations on an HA pair, and the question implies a default scenario, not requiring explicit pre-configuration for every connection.

The maintenance of connections is not differentiated by their longevity; rather, it depends on whether connection mirroring is active for the specific service, which it is for NAT by default.

This contradicts the core purpose of connection mirroring in a redundant BIG-IP system, which is to ensure existing connections are not lost but seamlessly taken over by the new active unit.