How quickly the character descends into the Abyss is really up to the player. Other than GM fiat, damnation is really only incurred by activating one's Vice.

To be clear, there are two entirely different scenarios that relate to your Vice. The first is a straight game-mechanical exchange – you activate your Vice power, gain its benefits (which usually involve manipulating a dice pool in some fashion) and also immediately gain a Damnation point. There is no other consequence and the game continues. The second is a pure role-playing scenario. If the Game Master presents you with a situation in which giving in to your character’s Vice will put you, other people (especially innocents), or the mission at risk, and the choice is significant from a story standpoint, then you are rewarded with a Hero Point for giving in to the temptation and thereby complicating the story. Giving in to your Vice has to make things tangibly worse if it is to be worthy of a Hero Point. Of course, as with so many other things in the game, what exactly constitutes “worse” is a matter to be negotiated between you and the Grand Master, but an example will hopefully clarify what we mean.