If any investigators are defeated during a round, does that decrease an epic monsters toughness, since their toughness is usually investigator's plus 2?

The other question I have is about end of Mythos actions. Can you solve the active mystery first before choosing new investigators? One mystery, I think is was Cthulhu's, seemed to be affected by the number of investigators that were out.

I do not believe the death of an investigator changes any needs based on the number of investigators as that player is still active in the game. This I believe is a one time check at the point of initial game setup. i.e. if the game starts with 4 investigators then the appropriate reference card is selected and locked for the duration of the game, all other requirements during game based on number of investigators then refer to the card.

I thought this was the case, just wanted to get another's opinion on it.

Besides, usually you'd pick another investigator to play

But kill off the epic monster before picking a new investigator at the end of the mythos phase.

ah I see the dilemma there.

Look at it like this: Once you choose your number of initial investigators, you put the card down that has the investigator symbol with the number of investigators on it. That card never changes, therefore when you look to see the number of investigators, you look at the number on that card. Because the symbol it is showing is on that card, and that represents the number you should be using. Even if an investigator is defeated, that number never changes.

Even after the ancient one wakes, that number doesn't change. So if after an ancient one wakes and an investigator is defeated, that number doesn't change even though you don't get to select a new investigator. It's unfortunate, but that's the way it goes. So that number is pretty much fixed from the beginning of the game.

That definitely makes more sense than having it constantly change throughout the game.