Why is Watch closed right now?

Watch isn't available 24/7 — it's open from 5:00 AM until midnight, and closed for those few hours overnight. If you open Watch and it tells you it's closed, that's expected behavior rather than a bug; it'll automatically become available again once it hits 5:00 AM. While Watch is open, you'll also see a small countdown showing how much time is left before it closes for the night.