I just need a bit of rules clarification that I'm confused about. If I Donate an enchantment to an opponent in a multiplayer game, and then lose the game myself, does the enchantment leave play with me or does it remain under the control of my opponent until they lose or the game ends?
When you leave a multiplayer game, all cards and permanents you own, including the ones that other players control, leave the game. Specifically, this means that the enchantment you Donated will leave the game. The relevant rule is 800.4a:
When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end. Then, if that player controlled any objects on the stack not represented by cards, those objects cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled.