Emergent Haunting’s first ability doesn’t have a duration, which means it remains a creature indefinitely.

At the beginning of your end step, Emergent Haunting’s ability will check to see if you’ve cast a spell from your hand this turn or if Emergent Haunting is a creature. If either is true, the ability won’t trigger at all. If the ability does trigger, it will check again as it tries to resolve. If either is true as the ability tries to resolve, the ability won’t do anything.