Some historians say that the reason for Abdullah Ibin Jafar not to leave Madina with Imam Hussain (PBUH) was that he had lost his sight due to a illness.
Others say he was asked by Imam Hussain (PBUH) to stay in Madina for the safety of the rest of the Hashimies (Bani Hashim) who were in Madina.
And some say he couldn't travel with Imam Hussain due to his old age .