Answer
This topic is explained in the introduction to Chaitanya-charitamrita. There, the author explains that he was requested by the devotees residing in Vrindavan to write about the philosophy of Krishna consciousness as taught by Sri Chaitanya Mahaprabhu.
At that time, Krishnadasa Kaviraja Goswami was living in Vrindavan, and the devotees approached him with this request. One may ask: why was such a request necessary when many books had already been written by previous acharyas explaining Krishna consciousness and the teachings of Lord Chaitanya?
The reason is that, although many authoritative works already existed, they did not systematically present certain specific aspects of Lord Chaitanya's teachings in the way that Krishnadasa Kaviraja Goswami later did in Chaitanya-charitamrita.
Therefore, he was requested to compose this extraordinary work. As a result, Chaitanya-charitamrita stands as the most comprehensive and authoritative explanation of Krishna consciousness as taught by Sri Chaitanya Mahaprabhu. The essential teachings, philosophical conclusions, and deepest aspects of Lord Chaitanya's mission are presented there in a systematic, authoritative, and beautifully organized manner.
For this reason, Chaitanya-charitamrita remains the foremost literature for understanding the teachings and philosophy of Sri Chaitanya Mahaprabhu.
Krishnadasa Kaviraja Goswami began writing this work when he was already very advanced in age. In the book itself, he mentions that his hands were trembling and his eyesight had become weak. Yet he considered it a miracle that he was still able to continue writing.
He was not even certain how long he would live, but by the mercy of the Lord and the devotees, he continued the work. Again and again, he attributes his ability to write not to his own qualification but to the mercy of the Vaishnavas and the Lord.
If you are looking for the specific verse where he describes these circumstances, you can find it in the introductory sections of Chaitanya-charitamrita. By searching through the text, you will come across the passages where Krishnadasa Kaviraja Goswami speaks about his advanced age, physical limitations, and the request of the devotees that inspired him to write this great masterpiece.
