Tom Robinson is a static character because he does not change throughout the novel.
Although Tom Robinson is an important character in the book, he does not change. He is a gentle, kind man and he remains that way throughout the book.
Tom is compassionate and submissive. In court he testifies that he felt sorry for Mayella Ewell and tried to help her out as much as he could.
“…I'd tip m'hat when I'd go by, and one day she asked me to come inside the fence and bust up a chiffarobe for her." (ch 19)
Tom is considerate enough to help Mayella, but he is a perfect gentleman. When she tries to make advances toward him, he rebuffs her at every turn—politely. Finally, she kisses him and he responds by running away.
I say Miss Mayella lemme outa here an' tried to run but she got her back to the door an' I'da had to push her. I didn't wanta harm her, Mr. Finch, an' I say lemme pass…(ch 19)
Unfortunately, Tom Robinson remains proud and compassionate. This is why he admits to feeling sorry for her, basically signing his death warrant. He realizes what he said was a mistake, because it will anger the white men.