This paper gives a proof that an adversial tetris AI can always force you to lose the game, no matter what you do. Interestingly it is enough to consider only left and right kinks (the S and Z-shaped pieces).
It does not give a proof that this must happen during a regular tetris game in which the pieces are chosen randomly, because the losing sequence is dependent on the player’s piece placement. It is not immediately clear whether a loss is forced even for a randomly chosen piece sequence.
Related is the Haetris game, a tetris game that tries to select the worst possible piece at each move. The default Haetris AI does not implement the above algorithm by Brzustowski, but it seems to be effective nonetheless, as nobody has found a loop yet.
qntm actually implemented the above algorithm in Hatetris recently! You can toggle the piece-choosing AI.