Does Lord Chaitanya appear in all Kali yugas or only in this Kali yuga?
Question, Hare Krishna. Does Lord Chaitanya come in every Kaliyuga or only in this Kaliyuga? Answer, Lord Chaitanya comes once in a day of Brahma in the Kaliyuga in which Krishna appears.
So, the Yugadharma is chanting of the holy names and that is taught in every Kaliyuga by the Yugavatar who comes. But that Yugavatar is not the combined incarnation of Radha Krishna. That Yugavatar is not teaching Madhurya Bhakti.
That Yugavatar does not give the Hare Krishna Mahamantra. Krishna has many names and that Yugavatar teaches Hrinamsankirtan and that Yugavatar is incarnation of Vishnu and that Yugavatar also has a golden complexion. But that is not Lord Chaitanya Mahaprabhu.
Sometimes he is known by the name Gauranarayan and he teaches chanting of the holy names which is the Yugadharma for Kaliyuga by which one can attain Vaikuntha but not Goloka. This is explained by the Gauri Acharyas in their commentaries elaborately. The important point is that the Lord's mercy is available through the Yugadharma and through the Yugavatar in each Yuga.
But the distinctiveness of Lord Chaitanya Mahaprabhu's mercy in terms of the highest revelation and entry into the highest abode is something which Chaitanya Mahaprabhu only gives. And after Krishna has come which is once in a day of Brahma nearly when half the life of Brahma is over so that is the time when Krishna appears and after Krishna appears and Krishna has revealed Goloka then Chaitanya Mahaprabhu appears and reveals the way to Goloka through Hrinamsankirtan. So the Yugavatar teaching the Yugadharma of chanting appears in every Kaliyuga but Chaitanya Mahaprabhu teaching the Hare Krishna Mahamantra and revealing the way to Goloka appears only once in a day of Brahma.