How do you deal with a very rude person? Specifically when you are unable to reply answers due to fear of losing something(job).

give him more respect and behave politely, if it does not work... increase the love dose ...

i would say that you could make a mix of this 

- kill him with your kindness and your polite answers 

- clear to him you would be glad to help him but he need to give you a chance so you can do your job in better way .

- be sure you understand the problem and solve it as quickly  as you can