I've had a long conversation with Fitbit support. They maintain that it's a phone fault, not an App or fault with the Fitbit (I have a Charge HR). They say that its a problem with bluetooth on the phone.
I've tried everything including reset of the Fitbit, uninstall and install app, turning bluetooth on and off - NADA. Strange thing though, when I first set it up, there was no issue at all, it's only in the last few days.
I'm returning my Fitbit as it's within 45 days, as I can't be bothered with the total hassle of this.
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