Do they disapear ( ie stop contributing to the agenda) if you defeat that enemy?

That is correct, they cease to contribute. Also if there are tokens on enemies when the agenda advances, you remove them to pay for the agenda. The same goes for the asset arcane initiate where if she goes out of play, she adds no Doom. If the agenda triggers, her token is removed from play.

To clarify further, ALL doom tokens are removed if the agenda triggers even if there are way more than the amount needed. Why is this important? Well say you are on the first stage of the first agenda in the first scenario, threshold of 3 doom. It currently has 2 doom on it at the beginning of the second mythos phase. Then while drawing, you get an enemy with a doom and a card that adds a doom and doesn't advance the agenda. You then play arcane initiate who has a doom token on it. Now there are 5 on board, at the next mythos a sixth one is added and then we check to see if we have 3 doom, which we do. Now all doom is discarded and the agenda advances, therefore meaning that you got rid of 3 doom without it contributing and the major drawback of having the initiate is now waved essentially.

And as a minor extra addition, the rule for removing the doom tokens is under "Leaves Play" in the RR, that says you remove all tokens. We had a hard time with that one because we kept looking for something specific to doom/agenda.