Weather can end a naval battle after the fleets have met

Have naval battles begun in fair weather only to be cut short by a severe storm?

Yes, many have; Trafalgar nearly became one, and its post-battle storm almost cost more ships than the fighting itself.

Sudden weather changes cut short numerous engagements in the age of sail. Weather also affected naval fighting during the Second World War. At Trafalgar, a storm arriving a few hours earlier could have interrupted the battle itself. After the victory, the same weather threatened or destroyed ships already damaged in action, showing that the sea could remain lethal after gunfire stopped.