Place this card in any space with an altar. If you end the round with 3 or more Monsters there, raise the Apocalypse Track by 1.
I can't seem to find anything in the rules that states that this card, doesn't stay in the same place for the full length if the game. Am I right?
It is only for the round in which it is played. At the end of the round, it is resolved and discarded. Per the rules page 24: "each Sin card should be kept in front of the Sins Players, and kept there until the end of the Turn. When the next Hero starts his Turn, move that Sin Card to the discard pile. and The Sins player can only play a Sin Card at the moment indicated on it, executing the effect described in the card and then discarding it.
In actual play, one usually keeps Hate! on the board so no one forgets about it, but the card is discarded technically. In fact, if say the Sin player had NO cards left and had to draw a new one, Hate! should be reshuffled into the Sin card deck, making it possible for it to be played twice in a single round.