I am a little confused by this one..

When a player is eliminated during the fight with the AO does that player's subsequent turns are skipped and you only just advance the clock?

For instance in a 2 player game the AO awakens at midnight and 1 of the players is devoured, until the next time the clock strikes midnight the last

remaining player has 2 or 4 turns to take?

The remaining player has 2 turns / day to take. Point is that the strength of the AO doesn't scale when investigators are elminated, thus you still advance the clock for the deceased

Thanks so much as always..