I have this nonsense going on with my Moto 360 Gen 2 paired to a Motorola Droid Turbo 2. For me it seems to be whenever the watch and phone get disconnected (i.e. I walk away from my desk at the office and leave my phone sitting there); when I come back in range instead of automatically connecting I get the pair message on the phone and watch again. Then sometimes it goes crazy and just enters a loop where it wants to pair every hour or so. I have no such issues with my LG Watch Sport paired to my Google Pixel XL running Android Wear 2.0, so I have to believe this is a problem with Moto's implementation on the 360.
Other problems include poor support for other/non-moto watch faces (that used to work perfectly with Wear 1.x), data for third party complications not working at all (i.e. Accuweather).
I was surprised when Moto released Wear 2.0 support because frankly I thought they'd given up, now I wish they had.