Normally I start checking after 9 pm the night before since cancellations seem to flood in before 12 midnight.
Like DLGal mentioned early AM works too but once they're gone [on same day] that's it unless Disney changes programing since you can't cancel same day. Those guests will just get a 'no show' if they don't go to parks.
Pretty much the only other time I've seen days stay open all day is in bad weather, or random slow day (very rare)