As I said recently in a slight different context, "careful craft will beat brilliant inspiration nine times out of ten. The true point is, of course, to yoke careful craft and brilliant inspiration together in a single process."
I'm going to go out on a bit of a limb here and say that I believe talent to be rather overrated. This is not sour grapes; I say this as someone who considers himself to be fairly talented at the narrative arts. But ability, taken here for discussion purposes in the sense of "craft", is what makes for successful writing.
Be assured I am not discounting the value of talent. It is possible to dazzle with sheer brilliance, and I'm rather pleased when someone can do that to me. But even sheer brilliance must still rest on structure, plot, character, setting, and all the other impedimenta of story-telling. Those are craft.
I can't teach you talent. You have whatever you have. Hence matociquala's "box it came in" theory, which I prefer to think of as the "hand of cards". There are ten or twelve or fourteen things that a writer needs to attain mastery of in order to tell a strong, compelling story. We all first come to the table with two or three or five of those things in our hands. Natural talent, in other words.
In my case, as a very new writer, long before I'd sold a word, or even written a comprehensible story, that was plot (though not endings), setting, and prose styling. Characters, on the other hand, were sort of people-shaped black holes for me, dialog was so clunky it hurt, my control of POV was laughable. Those things I had to learn. Craft, in other words, carefully attended to and practiced over the past two decades.
One of my personal challenges in growing as a writer has in fact been to recognize the limits of my talent, and from that where and how to apply my learned skills at craft development to those areas where I already considered myself pretty hot shit. (Ego isn't pretty, is it?)
I may not be able to teach you talent, but I can teach you craft. Or at least someone can, if it doesn't happen to be me. In fact, with one notable exception, I'm of the opinion that any aspect of craft can be taught, and if practiced well, mastered.
Another way of saying that is to aver that you don't need talent to succeed at writing. You need the ability to learn good craft, you need to attain facility at that craft (if not mastery, eventually), and you need psychotic persistence. Talent sure can help, and may be a handy shortcut for some of the cards of craft, but it can also be a dead end and a trap; much as I have experienced.
The notable exception? I don't believe I can teach you voice. Voice is one of those things that adheres to the Potter Stewart test - "I can't define it, but I know it when I see it." To my current thinking, voice is the distinct quality that makes you the writer you are, delightfully unlike everyone else. It arises out of the intersection of talent, craft, and life experience, and like the sea, voice is ever changing.
You have talent in whatever measure you happen to be granted it. Craft can be taught, and will bridge the gap between talent and achievement. Voice is the intangible fusion that moves you from practiced to good; and with luck and skill, from good to great.
So to speak to tchernabyelo directly, is there a limit on talent and ability? Yes, on talent, because it's an inherent quality independent of effort and focus. Potentially not on ability, because it's an acquired characteristic dependent on commitment and practice. You can't control talent, but you can control craft.
As I often say, "write more". That is the essence of commitment and practice.