There are several factors at work in what you're seeing. The first is that the skill bars are made up of "segments" and won't change until the villager has gained enough skill to move to the next segment, even though they are actually gaining skill with each successful task.
The second is that the amount of skill a villager gains with each task depends upon how skilled they already are. An untrained villager can show a noticeable change in the skill bar on the first successful attempt. As they become more skilled, the incremental change in their skill is smaller as their skill increases. Once a villager becomes adept, the amount of additional skill they gain with each successful completion of a task is much smaller than it was when they were trainees. It can take only a few successes to go from untrained to trainee, and hundreds more successes to make it all the way to master.
Finally, some villagers learn faster than others, just like real people. Each villager will gain skill at their own pace. Each time they succeed, they are gaining skill, even though you might not see it right away. Just give it some time and your villager will make noticeable progress.