Nami's W refreshes upon killing an enemy in the Fog of War.
At least twice in a custom game, I set my W to finish off a bot fleeing into the brush. Most cases, if you hesitate, the ability is cancelled because you don't have a valid target. Sometimes, if you're unlucky, the ability goes on cooldown but the ability never truly went. Anyway, in both instances, the bot ran into the brush and the missile chased after the enemy, immediately telling me the enemy has been slain. Strangely, her ability has refreshed, even though I had just used it.
Steps to recreate:
1. Get the enemy champion low enough for Nami's W to kill them.
2. Cast W as they disappear into the brush.
This happened very early in the game with a Philo Stone, so it was not a strange/new item causes weird glitches, and then once later in the game against different enemies. Rank did not matter.