http://starwars.wikia.com/wiki/Anakin_Skywalker’s_second_lightsaber

Shortly after this, Luke carried the weapon with him to the Cloud City on Bespin in a bid to rescue his friends from Darth Vader. Engaging the Sith Lord in a lightsaber duel, Luke demonstrated his vastly increased skill with the weapon, impressing its former wielder. Ultimately, however, Luke’s lightsaber hand was sliced off by Vader and fell, along with the lightsaber it carried, into the depths of Cloud City.[17]

The lightsaber, still clutched by Luke Skywalker’s hand, had become lodged in one of Cloud City’s lower air shafts and eventually was recovered by a maintenance drone. The drone deposited the hand and the lightsaber in Smelting Core D. There, it was discovered by Groggin, the Smelting Core’s supervisor.

In addition (and more importantly), I just watched the scene and there’s nothing to suggest the lightsaber fell out with him. There were even multiple shafts at the bottom so it could have fallen into any of those.

Next topic.