This happened with a friend of mine and I am asking this question on his behalf.
My friend was recruited for a sponsored research project in the university and offered a part-time PhD along with that. He is currently completing his coursework (2nd semester) which is pretty exhaustive. He has been working pretty rigorously and one of his poster presentation was accepted in a reputed conference within 6 months of work.
Since the coursework in this semester was tough, he wasn't able to give any tangible output in terms of publications or concrete results. Now, suddenly he has been asked by his advisor to resign. This has come to him as a surprise since he was expecting some scolding as his guide is known for being arrogant (and he is very reputed researcher in the field).
He is unsure whether to leave PhD or how to proceed and convince his advisor.
I believe he is pretty new (1 year of coursework) to the domain and since the project is pure research, he does deserve a chance. But I am unsure of how one should proceed in such cases.
EDIT (based on queries in comment)
Part Time PhD: He was recruited as an employee for the project by the university. And also offered a PhD. The stipend comes from the project cost(funding agency) and not from university funds (as is the case for direct PhD recruits in my university).
Advisor being Arrogant: He is very knowledgeable and reputed but known for scolding students frequently.(Some faculty members also agree to this including my own advisor)