I've noticed it on an earlier firmware/app combination and it seems to still be present with the latest app and Beta 4.07 firmware...
The Live Event Sharing options are deceiving between the watch and the Connect app. We are forced to use the app to set most of the settings up (message content, triggers, adding new contacts), yet it seems like the app's settings don't always take effect. I assume it has something to do with syncing between the phone and watch and which side wins for various settings (i.e. enable).
Last night I set it up on my phone and assumed with nearly 12 hours to my event that the settings I chose would sync down ok and be what I saw in the morning.
I checked the settings on watch 30 min before my race and noticed Live Event Sharing was off and the message content didn't look totally right (no estimated finish time, for example, which I had added last night). I turned on the Event Share using the watch gui, but then also went to the app and checked over the settings making changes where it seemed needed again.
I didn't triple check the settings, partially because both the watch and App were toggled to "Enable" so even in a missing sync it should be on (but maybe with message content differing from what I intended)
I started my race and realized during that event share was probably not working as I was not getting notifications for text messages while running (and I always have my own phone on the added phone list). Sure enough, at the end no text messages were sent out.
In the future I need to ensure the watch believes Event Share it enabled before starting, but in my experience the setup process between App/Phone for this feature is a total mess.