It's mostly impossible. You can't even drop a connection and reconnect on the SAME port.
You mentioned Attachmate, so I assume you have some kind of telnet-3270 gateway. You might be able to rig up something on the gateway. i.e. Telnet to the Gateway, and instead of auto-connecting via 3270 to the host, run a program like screen, or nohup, then 3270 in to the host. screen and nohup are unix shell apps that will allow you to disconnect and reconnect.