You cannot have your hearing aids connected to both devices at the same time, although they can be paired to both.
I believe that after you switch device, the latest device may attempt to take the hearing device connection from the other iOS device, if you enable the “Audio Handoff” option in the MFI Hearing Devices page. Now whether it can be done cleanly and successfully or not is another thing. I’ve seen it working before, where there’s a message popping up from the latest device saying something to the effect that it’s attempting to take over connection from the other device (only if the audio from the other device is not streaming to the hearing aids anymore). I’ve also seen it not do this, and I’d have to turn off the Bluetooth of the other device before streaming audio would get routed to the latest device.
Sometimes even THAT (turning off Bluetooth on the old device) wouldn’t help and you’d have to Forget the hearing aids from the old device before it would work on the latest device. It seems like this is what you’re experiencing.
My MFI hearing device is a pair of Oticon OPN 1. I have an iPhone 7 Plus and an iPad.