> Connections should only be closed due to? Inactivity.

Or if the user closes the browser of if the server/proxy restarts. But yes, mostly inactivity on the order of a couple of minutes.

> If a connection is closed, don't you think you would probably want to do another DNS request?

That's the whole point of the DNS TTL, to say how long to go before doing another lookup rather than doing it each time you reconnect.

> Also if your doing proper layer 4 load balancing using BGP, DNS is a moot point...

BGP load balancing operates on layer 3, and is irrelevant as you still need to DNS lookup an anycast address. EDNS client subnet is better anyways.