I recently ran into a problem where "Hey Siri" wasn't working on my Apple Watch. I was sitting there, calling out "Hey Siri" with increasing volume and Siri had no interest in me. In fact, I said "Hey Siri" so loud that I set it off on my phone, which was in the next room charging. MacRumors published an article that shed some light.

In order for "Hey Siri" to work on your Apple Watch, the screen needs to be lit. It won't activate when the screen is dark. If the screen is lit from you twisting your wrist or tapping the screen to wake it up or pressing the digital crown to wake up the watch, "Hey Siri" works. However, if you are in a glance or in an app, saying "Hey Siri" doesn't work. The above linked Mac Rumors article explains that if you are at the watch face as a result of pressing the digital crown from another view (like the home screen or an app), "Hey Siri" also doesn't work. However, in my testing "Hey Siri" worked just fine in that scenario.