It sounds like a Wi-Fi endpoint negotiation issue, possibly. If you’re running Zwift on a Mac and haven’t used it for a while, have you tried to toggle the network permissions on the Mac side? If that option isn’t available, you can reinstall Zwift and it should come back. There can be inconsistent connection behaviour between iOS and Mac devices without this. If the toggle is there, try to toggle it off and on to see if it sets the correct permissions to hold the network connection while the process is backgrounded.
See this: Companion App connection problems? [iOS 18] [macOS 15] - #21 by Ingemar_Bergmark