Why does my Garmin vivoactive not register my trail runs when going below a certain speed, eg walking up an extreme incline?

No, it's really strange, and very annoying  

Are you using  Move IQ to start and stop your activities? That could cause that behaviour. Instead start your activities manually.

No  

Which vivoactive do you have? Original, HR, 3, or 4?

When you say it doesn't register, are you saying the activity will not sync with Garmin Connect or does it sync under a different activity type? Does the activity exist on your watch and under the \GARMIN\ACTIVITY folder?

3. I've set my watch to run, so it's logging the run until the terrain is so steep that the only way is to walk therefore slow down, at which point my watch stops registering the run until I pick up my pace again.

Fantastic! Thank you, yes it was! I'm doing another high elevation tomorrow so I'll see how I go.