I am referring to the stage where someone reaches his/her capabilities limits, especially professional limits. I am thinking about career advancements as well as the growth in professional life. We all reach our limit in that progress and going further would be unnatural or might put us in a difficult position because we are not able to cope with a higher level of abilities or responsibilities. Is there a word or expression to define this limit in personal progress?
Medica's answer pointing to the Peter Principle is on the money, however just to add a phrase or two...
colloquially: maxed out, plateaued, sweet spot
Having "risen to his level of incompetence" refers to having gone beyond Jack's referred to territory of competence. "Out of his depths" would similarly express having risen above that territory.
Actually, you are describing the Peter Principle to a "T".
Formulated by Dr. Laurence J. Peter and Raymond Hull in the late 60's,
The Principle further states that the work of that person who has reached their level of incompetence tends to be done by those below him who are better equipped. Managing upward is the idea that a better-suited subordinate finds ways to subtly "manage" superiors in order to limit the damage that they end up doing.
On an very public level, the disastrous response by FEMA to Hurricane Katrina was shown to be the result of FEMA Director Michael D. Brown's being a victim of a poor promotion. Brown had excelled in his previous position, and naturally was given a job with greater responsibilities by President G.W. Bush.
This seems to match well your statement that "We all reach our limit in that progress and going further would be unnatural or might put us in a difficult position because we are not able to cope with a higher level of abilities or responsibilities.
Whether it has a more succinct or different name, I don't know. I've only ever heard this referred to as the Peter Principle.
You might describe it non-specifically: you've exhausted your potential, reached your limits of expertise, you'll be in over your head, etc.
That might be the most neutral, least provocative way of expressing this idea.
Are good suggestions from @MarkKasson, although they may be slightly pejorative.
Also from @MarkKasson's answer, is not correct IMO. This expression has nothing to do with reaching a limit - it simply means you've gotten something "exactly right"; "the stars were perfectly aligned"; "everything came together".
I am thinking about career advancements as well as the growth in professional life.
The Peter Principle is way off. You are describing a situation where you want to progress, right? Also, you say that it is 'personal progress'...?
If you are concerned about your own personal abilities to become a person who can learn to advance, or adapt to the demands of being more creative/organized/productive, then that is a personal development issue. You might be frazzled at your limit, and raising the bar might make you feel worse, as you would feel you couldn't perform at 100% even with your best efforts...
If you are concerned about your career being stonewalled, or hitting a dead end, or any of the other terms, then it is a matter of being the kind of person that will fill any void of opportunity. That is, you will get bored/sloppy/lazy if you go to work on auto-pilot.
I see a lot of folks stay in one position forever. They have a job. Others are completely unsatisfied where they are, and are continually moving up... They have a career.
Avoiding the risk of pissing off the moderators for ending an answer with a question mark (however professional/polite it is):
Ask yourself what type of person you are, and you will know what kind of professional you are.