I asked the same question 3 months ago. I am a Ph.D. student in mathematics and am suffering from a problem. My coauthor has not responded for 2 months, and as a result, I am unable to submit the paper without his consent. It has been almost seven months since I completed the paper and sent it to him. I am requesting that he proofread and make any possible language changes before submitting it to the journal. When I asked the same question three months ago, I got some of his reply, and he promised to finalize the paper (i.e., proofreading and language) in 15 days. But again, two months passed with no reply, even after four emails were sent to him. A total of seven months passed in this way.
He is a professor. We live in different countries, so no physical meeting is possible. We just met once at a conference. Despite our verbal agreement to work together on the project, let me tell you that I did all of the writing and editing for the paper, and he only assisted with proofreading, which revealed some errors that I then fixed on my own. I still offered him the authorship, and he accepted it eagerly.
Since it has been seven months and I have already mentioned it in my profile about the title of the paper, I have even cited that paper in my other new paper and have used some concepts from that paper, so I told him that even you have less time then at least submit the paper in some database like arXiv, etc. But he is telling, people can steal the work from arXiv, and that is why he doesn't prefer arXiv. I don't find it a very reasonable comment, though. In my opinion, he is very good in terms of ethics. He has good publications in reputed journals in mathematics. But very irregular in cooperation.
What choices do I have? Without his approval, I am unable to submit the manuscript to arXiv or a journal. However, I can't just leave the work undocumented for a very long time. To claim our work, it should at the very least be stored in ArXiv. Besides that, I am a Ph.D. student and I need publications.
Any suggestions would be helpful.
Edit: I live in Asia and he lives in Europe. So it not economically suitable for me to set up an in-person visit. This situation occurred before as well, he will not reply one or two months and then suddenly replied. He even proposed a post doctoral position to me if possible. But the question is even if he busy, he can just tell me that I will do it later so that I can be assured that he is in collaboration. About 6 months ago, i said him that my supervisor has read my paper and proofread on the language part, should I offer my supervisor an authorship, but he said not but we will acknowledge your supervisor. I agreed with him. This shows he doesn't want others to involve in the paper, but he is not doing the final action, completely keeping me immovable.