How long the Hare Krishna sankirtan movement will continue?
Kali-yuga is full of contamination. This is described in the Srimad-Bhagavatam (12.3.51):
kaler dosa-nidhe rajann asti hy eko mahan gunah
kirtanad eva Krishnasya mukta-sangah param vrajet
This age of Kali is full of unlimited faults. Indeed, it is just like an ocean of faults (dosa-nidhi). But there is one chance, one opportunity. Kirtanad eva Krishnasya mukta-sangah param vrajet: simply by chanting the Hare Krishna mantra, one can be freed from the contamination of Kali-yuga and, in his original spiritual body, can return home, back to Godhead. This is the opportunity of Kali-yuga.
When Krishna appeared, He gave His orders, and when Krishna Himself appeared as a devotee, as Sri
Caitanya Mahaprabhu, He showed us the path by which to cross the ocean of Kali-yuga. That is the path of the Hare Krishna movement. When Sri Caitanya Mahaprabhu appeared, He ushered in the era for the sankirtana movement. It is also said that for ten thousand years this era will continue. This means that simply by accepting the sankirtana movement and chanting the Hare Krishna maha-mantra, the fallen souls of this Kali-yuga will be delivered. After the Battle of Kuruksetra, at which Bhagavad-gita was spoken, Kali-yuga continues for 432,000 years, of which only 5,000 years have passed. Thus there is still a balance of 427,000 years to come. Of these 427,000 years, the 10,000 years of the sankirtana movement inaugurated by Sri Caitanya Mahaprabhu 500 years ago provide the opportunity for the fallen souls of Kali-yuga to take to the Krishna consciousness movement, chant the Hare Krishna maha-mantra and thus be delivered from the clutches of material existence and return home, back to Godhead.
Chanting of the Hare Krishna maha-mantra is potent always, but it is especially potent in this age of Kali. Therefore Sukadeva Gosvami, while instructing Maharaja Pariksit, stressed this chanting of the Hare Krishna mantra.
kaler dosa-nidhe rajann asti hy eko mahan gunah
kirtanad eva Krishnasya mukta-sangah param vrajet
“My dear King, although Kali-yuga is full of faults, there is still one good quality about this age. It is that simply by chanting the Hare Krishna maha-mantra, one can become free from material bondage and be promoted to the transcendental kingdom.” (Bhag. 12.3.51) Those who have accepted the task of spreading the Hare Krishna maha-mantra in full Krishna consciousness should take this opportunity to deliver people very easily from the clutches of material existence. Our duty, therefore, is to follow the instructions of Sri Caitanya Mahaprabhu and preach the Krishna consciousness movement all over the world very sincerely. This is the best welfare activity for the peace and prosperity of human society.
Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Eighth Canto, Chapter 5 – Text 23