That is an excellent question. The answer isn't really easy. Why does anyone willingly suffer abuse? There are myriad answers to this question. Perhaps, like many abused/repressed people, Invisible Man is hoping that if he pleases the abuser(s) they will respect him. In the Battle Royal, when all the fighters are eliminated except IM and Tatlock, IM himself says:
"I wanted to deliver my speech more than anything else in the world, because I felt that only these men could judge truly my ability."
This statement suggests that at this point in his life, IM does not respect the values of his own race. He is looking towards white men for validation. He thinks that only they (who are at that very moment abusing him and behaving like beasts) have the ability to judge him--and he desperately wants to meet their standards. At this point in his life, he feels that only white men count. And he knows he must accommodate them if he is to stay in their good graces. Of course all of this occurs before he becomes invisible.