Sea conditions are crucial. Ferries might be cancelled if there are strong winds.
Clear sky
Yes, it can happen: in rough seas or strong wind, operators delay or cancel departures for safety. If you booked online you'll typically be offered another departure or day, or a refund — and you're notified of the change, one more reason to book ahead instead of chancing the ticket booth.
As a reference, when the wind exceeds ~30 km/h this page flags it in red: with that warning, expect possible changes. If the day looks doubtful, the crossing from Santa Pola is the shortest (15-20 min) and the least affected by the sea.
Check this page on the morning of your trip and review the timetables by port. More questions answered in the FAQ.