You should not ask. It is extremely unlikely to produce anything useful, but will probably make the interviewer uncomfortable. Instead, try to arrange for a mock interview with a mentor who is familiar with your background, and get feedback from them.
Many potential weaknesses would require long-term actions for improvement or are even unchangeable, and thus feedback there isn't going to be actually actionable for you. Better grades in your previous studies, more research experience, etc.
The most useful information for you would be situations where you've failed to bring your existing strengths across. Learning of this is immediately actionable for your next interview. But an interviewer cannot identify these situations, because by definition they remain unaware of the relevant strength. Keep in mind that PhD admission interviewers are trying to determine whether you are a good fit for their PhD programme, not whether you interview well. So if they can isolate a pure interview mistake, they'll probably attempt to correct for that anyway.
Besides the issue that discussing someones failure is awkward anyway, interviewers might also be worried that you want to hear the reasons for rejection not in order to improve yourself, but in order to either argue with them about the decision or to appeal it. Given this risk, and given the difficulties in providing useful feedback, I suppose that you'll hear some variation of "Unfortunate we cannot provide detailed feedback to unsuccessful candidates. We wish you all the best in your future endeavours" if you ask.
(I would expect my answer to be broadly applicable, but my concrete experience with this is UK-based.)