I'm having the exact same issue. It all started last Thursday night at dinner time. My watch would vibrate every couple of minutes because my watch face has a notification to vibrate when it loses BT connection. Prior to that I rarely have any connection issues.
At first I thought it was my phone, but I have BT headphones and they connect fine and it can play music for hours.
You might be right about the Power Saving issues. My Pebble time steel would disconnect, after putting my phone down for a few minutes, but it'll reconnect when I unlock my phone to use it.
Spooky.. Thats pretty much exactly what i have seen. Mine also started on Thursday, but i didnt actually realise that anything was wrong until the weekend.
in my case, it got worse to the point where i had to go into the Pebble Time app and hit "connect".
i have disabled the Power Saving settings and so far today, i havnt noticed a single disconnect.. So i am hopeful.