Relationship to the person
Sometimes a man walks away from a conversation because he is disturbed by his companion. If there is hostility against any person, there is a desire to stop contact with her. Negative emotions can cause personal qualities, the nature of man, his words and actions. Sometimes the impression unkempt appearance or odor.
Some individuals are too intense. Such urgency causes irritation and the desire to get away from the conversation. It turns out that the conversation stops because of the annoying-ness of one of the interlocutors, which tend to leave the surrounding under some pretext.
Insincerity
Maybe the person away from the conversation because he did not want to disclose some information. If he has something to hide, it will try to sneak out. When you find yourself in this situation, you can't conclude that before you is a compulsive liar or some kind of attacker. Maybe the reluctance to answer a question caused by deeply personal reasons.
Some people are just not used to open up to others. If the conversation goes too far, they become unable to continue it and try to quickly retreat. Take it as a part of the personality of the interlocutor. Do not expect that everything will be sincere with you, even if you openly and honestly talk about yourself literally everything. Remember that everyone is different.
Uncomfortable topic
Try to carefully choose topics for conversation. Some people are so don't feel a certain line in the conversation that I ask others absolutely tactless questions. Few people can like discussing intimate details of their own lives with the unfamiliar man.
Also there are topics that are taboo to discuss in society. Such issues include: religion and religious beliefs, financial situation, health. If you are curious on one of these topics, don't be surprised that you do not respond. When you want to have a conversation with you supported, choose a more neutral items for discussion.
Sometimes you refer to a person as an expert with a specific question, and he goes on talking. Here it may be that your consultant just not competent in this matter and does not want to directly admit it. When you don't clearly answer your question, it is better to consult other authoritative person.