You can concede a game while Platinum Angel on the battlefield. A concession causes you to leave the game, which then causes you to lose the game (Once you concede, you no longer control a Platinum Angel, so its ability can't prevent you from losing the game).

Effects that say the game is a draw, such as the _Legends_(TM) card Divine Intervention, are not affected by Platinum Angel. They'll still work.

If you control Platinum Angel in a Two-Headed Giant game, your team can't lose the game and the opposing team can't win the game.

No game effect can cause you to lose the game or cause any opponent to win the game while you control Platinum Angel. It doesn't matter whether you have 0 or less life, you're forced to draw a card while your library is empty, you have ten or more poison counters, you're dealt combat damage by Phage the Untouchable, your opponent has Mortal Combat with twenty or more creature cards in their graveyard, or so on. You keep playing.

Other circumstances can still cause you to lose the game, however. You will lose a game if you concede, if you're penalized with a Game Loss or a Match Loss during a sanctioned tournament due to a DCI rules infraction, or if your _Magic Online_(R) game clock runs out of time.