Just changed phone from Moto X4 to a Nokia 6.1 androidone.
If I was out of range and then came back with the X4 it would reconnect with no issues. With the 6.1 it will not reconnect at all unless I go into Bluetooth settings and tap on the gear S3 in the paired items list to manually reconnect.
The 6.1 is running Oreo 8.1 with May security update.
All software that is needed is installed and up to date, I have used this watch with no connection issues on 3 other phones at least so I have a generally good idea as to what I'm doing.
I have also posted about this on Nokia's support forum, so I'm reaching out to both sides of the problem.
I've got the same issue with my Nokia 6.1. My previous phone connected to my S3 without issue so it seems to be an issue on Nokia's side. Have you heard anything from them?
Sorry, I'm afraid not. After 3 weeks of being fed a line of bs from Nokia support I gave up and took the phone back to the shop. Glad I did in the end as it seems the variant I had (TA-1050) still has problems with being updated from what I have seen, people have had to do hard resets and use a VPN to get their phones updated, and still no Bluetooth fix. I ended up getting a Huawei P20 lite, it cost a bit more and it's not an androidone handset but it has been massively more reliable and my gear s3 connects without issues.