Unfortunately I don't understand the formulas enough to tell you where you went wrong, but I can logically explain why your answer is incorrect.
From deuce there is a 36% chance A will win the game a 16% chance B will win and a 48 percent chance the game will return to deuce.
Once the game is back at deuces there is again a 36% chance A will win, 16% chance B will win and a 48% chance the game will return to deuce.
Therefore each time two games are played there is a .48^n chance that the game is back to deuce. Since this number is less than 1, as n apporaches infinity (the case we're talking about here because we want the game to end) the probability of being at deuce approaches 0.
That said, every time the game was at deuce the same probability existed for A or B to win, so the overall chance for them to win is proportional to the 36 and 16%. 36% is to X as 52% (16 and 36) is to 100. X is roughly 69%, or exactly 9/13.