Zero downtime deployment with f5 GTM+LTM ?.

If the action on service down is set to none, then you should be able to bleed active and persistent connections, depending on what the pool members are set to. If GTM is using the bigip monitor for your LTMs, then new DNS lookups will lead to a different answer and thus a different VIP than the previous answer, but that should only impact new DNS lookups by your client's name servers.

If I were troubleshooting this actively, I'd take a packet capture on a client machine where the behavior is repeatable AND the BIG-IP where the servers are being shut down.