If the athlete cannot complete all programmed reps, a reduction in volume is usually needed. This is assuming that the athlete is eating and resting enough. This is important. If recovery is not addressed, then this will naturally limit progress in strength, regardless of the actual programming. Make sure diet and sleep are in check.
When reps are missed (or if a 5 rep set becomes extremely difficult, resulting nearly missing a rep) this usually occurs on Friday's intensity day. When this happens, programming 2 sets of 3 reps at the same weight (if 5 reps could not be achieved) or 5 lbs heavier (if 5 reps were achieved in the previous week with much difficulty) can usually yield a few more weeks of progress. As progress within the 3 rep range stalls, the athlete can do 2 sets of 2 reps at the same or heavier weight. This may yield another couple weeks of progress. As this stalls, the athlete can finally move to 5 sets of 1 rep (i.e. singles), then, once this becomes very difficult to achieve, 3 sets of 1 rep.
Once 3 sets of singles stalls out, the athlete can use that weight as their '1RM' and begin a new cycle of 5 rep sets. After another attempted cycle of Texas Method, more advanced variation needs to occur on the Friday intensity day. This is explained in depth in Practical Programming and is outside the scope of this post.