Actually a single score can and will affect your handicap index and will affect it for one year from the date of the low round. If a low tournament round exceeds your handicap index by three shots or more, your handicap index will be reduced to jibe with the low T score. So one exceptional tournament score becomes a part of your handicap for the next 12 months, immediately affecting your current handicap and the next 12 months of revisions.
From the USGA:
Tournament Scores (T-Scores) are kept for a minimum of one calendar year from when they are posted.
The most recent twenty (20) scores as calculated are weighed against the average of the two best T-Score differentials, and if the difference of both T-Score differentials is at least three strokes lower than the Handicap Index (as calculated from the most recent 20 scores), the player is eligible for a reduction.