Is it best to aim for a set number of repetitions and fall short of the goal, or is it better to reduce weight to allow yourself to maintain achievement of that target rep count for each subsequent set as fatigue increases?
You should be following training protocols specific to your goals or to that of whatever program you are following. Within any strength training set, you should be working to (or close to) failure as this will sufficiently challenge your muscles to produce the best stimulus for growth (size and strength). When you are given a certain number of reps as a goal for each set, you should adjust the resistance accordingly.
If your goal is purely strength, then you should give your body enough rest between sets to be able to reproduce that first set again.
If your goal is purely stamina, then you should give your body minimal rest (60 seconds as a general upper limit) between sets and continually drop the weight for each successive set.
If your goal is somewhere in between, then your training protocols will lie somewhere in between.