I had the same problem with the HRM dual on Android. It seems to be some internal “hidden” state on the phone. Using the iPhone “Reset Network Settings” may fix it. On Android I could back up network settings (making sure the HRM was not paired) and restore after resetting but I don’t know if you can do that on the iPhone, so make sure you have WiFi passwords and such saved.
Also some people had it work after updating firmware on the HRM, but I don’t think you can do that unless you have a Garmin device to pair to it.