The reason Rishis aren't born in the Kali Yuga is due to transgression of Brahmacharya, as described in this chapter of the Apastamba Dharma Sutras:
The word 'austerity' (must be understood to apply) to (the observance of) the rules (of studentship).
If they are transgressed, study drives out the knowledge of the Veda acquired already, from the (offender) and from his children.
Besides he will go to hell, and his life will be shortened.
On account of that (transgression of the rules of studentship) no Rishis are born amongst the men of later ages.
But some in their new birth, on account of a residue of the merit acquired by their actions (in former lives), become (similar to) Rishis by their knowledge (of the Veda),
Here is what Haradatta says in his commentary on these Sutras:
Amongst the avaras means "amongst the men of modern times, those who live in the Kaliyuga." No Rishis are born means "there are none who see (receive the revelation of) Mantras, Vedic texts." ...
How is it then that men in our days, though they transgress the rules prescribed for students, learn the four Vedas with little trouble? (The answer is), By virtue of a residue of the reward (due) for the proper observance of those rules (of studentship) in a former Yuga. Therefore Âpastamba says, Sûtra 6 "But some," &c. New existence means "new birth (life)." ...
Like Svetaketu. For Svetaketu learned the four Vedas in a short time; as we read in the Khândogya Upanishad (Prapâthaka VI, 1).
I discuss the Apastamba Dharma Sutras' statement about Shwetaketu in my question here.