A while back I had an issue with Bluetooth not connecting properly when more than one device was involved. Although the devices are different than in your case, (and I don't have an iPhone so I don't know what you're looking at) but maybe there's something in what I found that may be of help. Here's what I reported back then:

A new Bose Soundlink Mini that I had been using with my iPad via Bluetooth worked flawlessly, connecting without issue.

The I coupled the Bose with my iMac and it worked fine.

However, the iPad then stopped linking with the Bose, instead suggesting that it needs to be within range, even though it was only a foot away. My Apple keyboard connected as usual.

I assumed the Bose might still be linked to the iMac so I opened the iMac and disconnected it. For good measure I also turned off the iMac Bluetooth.

Still no connection....just the dialogue box about range.

The I found this suggestion on the web: "Clear the list on your Bluetooth® device. For more information, please refer to the manufacturer of the device".

So, on my iPad Settings/Bluetooth/Devices I selected the Bose SoundLink Mini and then the "i" for information. In the new dialogue box I choose "Forget This Device". A new search attempt worked perfectly.


ryck

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