Apple Watch Series 3 Will Not Pair

Update: I tried two more handsets, same result. I even tethered my phone to my other phone to eliminate my home network, same result but I did not get the 'unable to verify as you're not on the internet' message. So, it's not the phones, it would be a huge coincidence if both watches failed in the same way despite multiple factory resets, and it's not my home network, and that only really leaves the update itself as being at fault. I have seen other anecdotal evidence that lack of space on a watch can cause this behaviour (and I always had to unpair both watches to update them anyway). These are both 4GB devices too.

Spoke with Apple support, they tried to convince me they had both watches were faulty (not sure i'm going to buy the suggestion that two factory-reset watches kept in their boxes for 6 months have developed identical faults), but did book me a slot with the Genius Bar. They have sent both off for examination (without charge) to try to understand more about what the issue may be.

Other respondents - do you know how much storage your devices have, and which models? I always had to unpair my watch (as did my wife) as the 3.9GB free space was not enough for any of the updates. Our son's A1858 GPS-only allegedly has 16GB (but only shows 8GB) and is the only one to update. It has not been unpaired though, unlike the other two. His watch is a year newer than our A1859s (also GPS-only). I'll report back when I get a response from Apple.

Apple's response - 'could not replicate fault' on both watches, and both came back running 8.7.1, free of charge. It took 5 days from Genius Bar to back in my hand, thanks Apple, excellent service. Sadly, I'm still none the wiser about why they didn't upgrade at home, even though my son's did, nor why the 4G update attempts failed. Sorry I can't offer anything else.