You should be prepared for a source who is unwilling to answer your questions and says so. In a sound recording for television or radio, their refusal to answer, whether directly said or indirectly implied, will be heard and can be skilfully used in your edit. In print, you can write: “X declined to answer questions about…” What you write should not interpret the failure to respond – just report it. The meaning of the refusal is for your audience to judge.
A point-blank refusal to answer legitimate questions may prompt you to abandon the interview. Sometimes this can be effective. You might say, “I am really sorry, Minister. I had not anticipated that I would not have input from you on these issues, which are at the core of my story. I will now only have my observations and the experts’ and witnesses’ comments to work with. Shall I just say that there is no comment from you?” At this point, an intelligent interviewee may decide it is better to say something than to be cut out of the story altogether. But if they still refuse to cooperate, leave politely.
If you are told in advance that certain questions will not be answered, it may still be better to put all your questions regardless, and make this clear. This is especially true in broadcast. Both your interviewee and your audience know that you did at least ask. If you do not, you are open to the criticism that the question was never put. Your interviewee may well claim later that he would have answered if only he had been asked.