Depends on the mesocycle and how many reps I'm off. In Meso 1, I'm looking for endurance. If I top out at 6-10, I hit pause, reduce weight, rest briefly, and try again. If that happens two weeks in a row, I recompute the 1RMs. If I hit 15 and don't feel tired, I'll pause/increase/rest and retry. Except shoulders.
In Meso 3, I'm looking for strength, so if I can only get to 6 and the goal is 7-9, I leave it alone and feel good about trying a challenging weight

If I could only get to 3-4, I'd rest, lighten, and retry ... unless the muscle is twinging, in which case I'd leave it alone. Also, deadlifts. If the reason I couldn't make a lift is a tired lower back, I just stop and don't do them again that day.
Meso 2 is in the middle - hypertrophy - and I would stop and pick up a heavier weight if it seemed obvious I was going to be able to go beyond 14, and I'd pause, rest, lighten, repeat if I was below 10.
Those numbers are more estimates, btw, not hard and fast. Mainly what I like to do is get in the rep range for the workout goal as much as possible. If the failure to meet reps happens towards the end of an hour, I might also just put it down to muscle fatigue unless it happened two weeks in a row. If earlier, I'd be more apt to rethink the weight.
This is only my second time through STS as designed, but I used parts of the various mesocycles through much of last year and this approach worked really well for me then.