I've had my Apple Watch for about a week and I use Siri constantly. For the first few days it worked like a dream: I'd raise my wrist, talk, and Siri would do what I asked. For the past few days, however, it sits there still listening after I finish talking. It'll remain in this state for upwards of 30 seconds - long enough that I have to tap the screen to stop it going to sleep and losing what I'd said - before finally deciding I have stopped speaking, and successfully doing what I'd asked.
It's not background noise that's causing this: I'm using it in the same environment that I'd used it in before, and it works perfectly on my phone.