I've done a bit of bug tracking earlier, so I know a thing or two how to approach issues.
The Mobile branch is still on development (Insider ring) and not yet released (I think MS calls the released versions Current Branch..) and there are a few BT issues. For instance when disablling the BT from the quick actions, it froze the UI for a minute or two - with the current Slow ring I'm on (10.0.14393.67) that issue seems to be fixed, but I'm not over confident about the general reliability of the BT still in the Insider preview builds. So this might be an issue with the current early access also.
Sometimes, when Pebble Essentials tries to open a BT connection, the connection will remain, but no notifications are forwarded. I believe this is not because of PE, but a bug in the Mobile BT stack.
I opened PE and closed it by long pressing the back button, ran the same timer twice in under a minute and both notifications were forwarded to the Pebble.
I got some issues with the notifications earlier today, so I turned the BT on and off from the phone, so it seems to me that it's more of an issue with the W10M BT stack, than the implementation of notifications in the PE. I'll keep logging events as well as I can.
I just installed the app to my laptop and will do some testing, I'll report if I find anything that's not working.
Glad to be of any help, I appreciate your work on the app a lot!