It depends on a lot of factors.
I noticed the same thing in the past, as I wasn't able to progress very fast if I was trying to add weight to the bar every workout.
What I started doing was keeping the weight the same for a whole cycle, and instead add reps each workout.
I started with 25 reps per exercise, regardless of how many sets it took me. During the first week, it looked like this:
Then on week two, I upped the volume to 33 reps, and week three and four I was going for 40 reps.
Im on week 4 now, and most of my exercises are like this:
But some of them im able to go 15, 12, 8, 5.
I noticed a huge progression in my ability on the first set, but not necessarily on all the sets after the first one. The first set is directly related to strength, while each set after that is more dependant on recovery from fatigue.
I keep the rest periods short though,(around 60 seconds) so im not trying to fully recover between sets.
I noticed you mentioned someting about being able to go for 12,12,12. IMO, unless you are training for performance, you should never be able to do the same number of reps on sets number 2 and 3, as set 1. If you can get the same amount on all sets, you are either resting too long, or not working close enough to failure on the first set.
I know your real question was about rate of progression though. You should be able to do more each workout, or at least each week, not necessarily more weight, but more volume or shorter rest. If you are not able to, you need to do shorter loading perdiods, and greater backoff periods.
Hope this helps.