What to do after receiving poor academic recommendation(s) I was recently applying for a number of PhD programmes, and I asked a number of my previous professors for recommendation letters. 

However, after the results of these applications were released, it was found that one of the professors has written a clearly negative recommendation (in comparison to the others), despite the fact that I felt that the academic relationship was good and on comparable levels to the other professors, and that he specifically agreed to write me a strong recommendation letter. 

I even noted in the request letter that "If you feel that you would not be able to write me a strong letter of recommendation, you should feel free to decline to write a recommendation". As other questions on this site have shown, it is not generally considered good form to write a negative recommendation, whatever the reasons.

I came to know about this, because the said professor submitted a number of recommendations late, and one of the interview requests from one of these universities was withdrawn, with the admissions department stating that it has been withdrawn after "reviewing recently submitted recommendations". 

Furthermore, after speaking with some of my other recommenders regarding my other interviews and asking for advice regarding further steps, they mentioned that they received calls from admissions departments regarding "inconsistent recommendations". 

As someone who would like to understand what went wrong during the process, what would be a good course of action in this situation? Should I approach the said professor and ask what went wrong, or would that not be a socially acceptable action?

I believe any answers should probably be relevant across all fields, but I am personally applying for a PhD in the US in the biosciences field.
Your professor either wrote the good recommendation they promised, in which case they are probably as shocked as you are, and happy to discuss what might have happened, and what to do now; or they lied to your face, in which case I wouldn't worry if talking to them is "socially acceptable." I don't know what would be the best course of action if the second is the case, but my first step would be to talk to them in person - just don't assume beforehand that it's one or the other, to make the meeting productive.

As two comments pointed out, there's also a (small?) chance that the professor meant to write a good recommendation, but failed at it. If that's even remotely a possibility, as well as probably in the first case above, it might help if they contact friendly faculty (should there be some) at one of the universities applied to, to better understand where the bottleneck is (within what is possible, considering the confidentiality of the process). Given that a letter-writer usually has some interest in the student they write a letter for succeeding, I wouldn't dismiss the idea before bringing it up with them, if appropriate.