I think I know what my Omnias are doing in the most extreme form of disconnection from my iPhone 14 Pro Max, i.e. when neither force-killing and relaunching the ReSound Smart 3D app (not recommended by ReSound as a good thing to do) nor rebooting the iPhone works to re-establish HA connectivity. In such a disconnect, only turning the affected HA('s) off and on again re-establishes iPhone connectivity for me.
For me, such a disconnected Omnia seems to have gone into Flight Mode, in which all Bluetooth is turned off. If one reads the Omnia manual, the way to exit Flight Mode is to turn an HA off, then on again. And that’s what re-establishes connectivity and HA BT broadcasting for me.
For me, disconnection seems to be triggered by “iPhone separation.” If I leave my iPhone somewhere and stay away from it for a fairly long time (>10 min) by going outside into the yard or by going to a far corner of the house when I return to the iPhone, that’s when I’m most likely to enter the Flight Mode-like state. The HA’s are still functioning ~normally in letting me hear room sounds, but because there’s no BT, they can’t be controlled by my iPhone, and they don’t show up as connected in Settings, Accessibility, Hearing Devices, MFi Hearing Devices, either.
They also don’t show up as broadcasting in the Smart 3D app Find My Hearing Aids applet: no signal strength is registered on the meter for any disconnected HA. Any disconnected HA doesn’t show up as broadcasting Bluetooth in any of three iPhone BT scanner apps: nRF Connect, BLE Hero, or BLE Scanner. As soon as an affected hearing aid is turned off, then on again, the rebooted HA shows up broadcasting Bluetooth as it should in all of the above tests, including the Find My Hearing Aids applet and in MFi Hearing Devices. I will write GN Support that they seem to have a very annoying bug in Omnia firmware. If it’s something caused by interacting with iOS 16, ReSound needs to get with Apple and literally iron out the bugs.
I don’t know if there’s any relation, but I found a separate Omnia Flight Mode bug that I’ve discussed in another thread. Normally, in the standard setup of the ReSound Smart Fit fitting software, the ability to enter Flight Mode is not enabled by default in the U.S. The FAA no longer requires hearing aid users to turn off BT connectivity in flight. When I have the ability to enter Flight Mode enabled for my Omnias, I cannot deliberately enter Flight Mode in the prescribed manual way for Omnia 962s with disposable batteries. That is, open and close the battery door of an Omnia three times within 10 seconds. Both of my Omnias, when I do that, still remain in normal operating mode, broadcasting BT by all of the above tests. Resound Omnia 961 rechargeable versus 962 with 13 zinc-air battery - #24 by jim_lewis
So that’s hilarious. 
I can’t enter Flight Mode when I want to, but accidentally, about once a day, usually during an “iPhone separation,” one or both of my HA’s may decide to enter a state functionally akin to Flight Mode.
So, @stu, if your wife has rechargeable Omnias, if Flight Mode entry were enabled by her HCP in Smart Fit, she could enter and leave Flight Mode in the following way (from the manual for the rechargeables):
Turning off wireless communication (activating Flight Mode)
- Turn off your hearing aid.
- Press the button for 9 seconds.
- Your hearing aid will double-flash four times. If you are wearing your hearing aids at the time, you will hear
double tones ( ) for about 10 seconds, meaning the hearing aid is now in Flight Mode.
Activating wireless communication (turning off Flight Mode)
- Turn your hearing aid off and then on.
- Wireless communication will be activated after 10 seconds.
It would be interesting to know if your wife’s rechargeable Omnias can be deliberately put in Flight Mode. Maybe there’s a ReSound/Apple MFi BT connectivity bug that prevents the deliberate triggering of Flight Mode but causes Flight Mode to accidentally occur at random times, perhaps triggered by “iPhone separation?”