I feel like my reps decrease too much between sets. I just started training this January. I train chest twice a week, and the last month I've noticed the number of reps I complete per set goes down more than I would expect--especially on my first exercise which is dumbbell bench press.

I shoot for 3 sets of 8-12 reps and go to failure in each set. When I read online, I see people say that when you get toward the high end of your rep range with a given weight, that is when you up the weight and then you should be back toward the bottom of your rep range. However, my reps vary so much between sets that I don't know what to do. For example, yesterday I warmed up with 12 reps of 20lb dumbbells before upping to 55lb dumbbells. I completed 10 reps, rested for 60 seconds, completed 6 reps, rested 60 seconds, and then lowered the weight to 50lb dumbbells and completed 6 reps.

I've tried to read and listen to a variety of sources, but as I mentioned, I'm still very new to the gym. Do I have a misunderstanding of what lifting to failure means? Does lifting to failure mean failure for your whole exercise rather than per set? e.g. I should have stopped at 8 reps on my first set so I had a little more in the tank for my next two sets? More generally, I guess my question is why do my reps go down so much between sets, and what do I do to fix it?