I believe I have solved this problem! (At least I have not missed a notification on my watch since I made the changes)
What I found is that my Settings across all my iOS devices were not consistent; in particular I recently bought a new iPad Mini (and I never seem to let go of the old devices, so I have iPhone SE (original), new and old iPad minis, and an ancient iPad.
I noticed that my iPad mini had "grabbed" a text even though it was in Lock mode (and neither my watch nor iphone received that text). So I poked around at settings to look for inconsistencies.
SETTINGS --> MESSAGES --> (and I went through all settings here for all my devices)
Inconsistencies for me were
"Start New From" -- all devices other than my new Mini had my @me.com account there; the new Mini had my cell phone number. I changed this to match the other devices and have not had a problem since!
"Send/Receive" -- I also noticed my old iPad didn't have all 4 options changed so I changed that to be consistent (not good practice to change more than one thing at once, muddies the process, but I couldn't resist)
ANYWAY - perhaps this may help someone else having similar problems.