Personally, I lean heavily towards the category under Cory's #3 earlier, it's drawing attention. But my first thought then is whether the sword's abilities are apparent in a way that others will be able to tell whether it's the sword or the wielder that is so notable. If the sword is known, or glows, for example, then others will hunt the sword. If no, then maybe the character is now considered a challenge and a target.
Either way, it can lead to other adventurers (or victims' families, or the church, or...anyone) coming after the party. When they are coming at the party knowing the character's abilities, they would come prepared - Charm, as someone suggested, or other spells (do they want to be lethal?), missile weapons they can use before the character closes with the sword, fighters who excel in disarming, and someone who can then teleport the sword away, or layers of distraction or deception and the sword is lifted by a thief. Any of those will allow the loss of the sword, temporary or permanent. Be prepared for the player to turn this into their life-goal, though, and have a recovery adventure ready.
If you truly want it gone, avoid anything that will specifically target the weapon, if at all possible. That becomes too personal, to a player, as others have said. An opponent or situation that does jeopardize all weapons or items equally, and doesn't care if they're enchanted, is more balanced and objective to the player. I've had fights on ships, with unstable footing and wet decks. Anything dropped has a high chance of going overboard. And a sword in the ocean on the high seas is either gone for eons, or another great plot line for an adventure. How well does the barbarian swim? Would he let a mage enchant him to act underwater? What kind of being found the sword and can effectively wield it down in the deeps?