Hopefully they have solved their problem. I would say to make sure you have the appropriate email client checked in the gear manager. if you are using gamail then make sure that one is checked and so on....
Re: Why does my Gear 2 Neo say "No Email" when I go to the email app on the watch
Gear 2 Neo you can't do that. You only have notifications. You have to read the entire email and reply on the phone. It's enough for me, but some may want more. I installed Flesky for replying to texts and it's way too small for me to type on anyway.
I'm running kitkat and whenever my phone starts up from a reboot or powered off state, I have to go back into Gear Manager and turn notifications back on to ensure I'm receiving my push notifications to my Gear.