I’ve been having a similar issue on my iPhone12 Pro on Alaska wifi. I get the login screen once. I click inflight messaging option. I close the screen out nothing works. In settings the wifi network shows internet not available although it is on my iPad. I’ve rebooted, turned off private WiFi network and can not connect again for the rest of the flight on my phone. Next flight I get a chance to do it all again. But no chance until my next flight. Yes my iOS is up to date.