Comment 10 for bug 2000798

I revisited this and have apparently found a way to work around it.

The keyboard can be reset, which I understand to mean that it forgets pairing information. The following sequence of keys resets it:

<Esc>
o
<Esc>
o
<Esc>
b

You should see all 3 lights turn on, signalising that the reset was successful. After that, I paired the keyboard with my phone and both of my laptops without issue, including the laptop that refused to connect to the keyboard for the last year or so. (What a relief!)

As a reminder, to pair device #1 to the keyboard, press and hold F1 for 3 s, until the light starts to blink. Then connect to the keyboard from device #1, enter the confirmation code and you're done: repeat for the remaining 2 devices.

Given that the workaround seems unrelated to the computer on which I've had a problem, I believe this bug can be considered closed.