Sonic has Amy for a very long time. Still he does not make a move but also run away from her. May be the word "Damsel in distress" cannot be used on this couple because both are true fighter. Still Amy is a girl and had a broken point. Furthermore , she tend to prove useful to him every battle. She's got thumb up from him but no hug even once.
My theory , he hates her. No solid prove on this but cannot neglect the probability. Or he just see her as a friend only and all along. Or he's already choose his soulmate and she's not Amy. Or he's gay!! LOL Well , Amy always believe in him no matter what he did she's always at his side and never falter her faith on him. She always cook for him. Celebrate him , praise him , tend his wound , rescue him , block the attack for him , look for him care for him. I feel like Amy is some kind of Love Slave and that's not fair to her. The blue always run away with annoyance everytime she come to him. If he give her free hug once a month would stop her from cracking his ribs.
But I look further at a time when she no longer be a pest to him. Which means "Death". I find no reaction more suitable than this. When she cling to his arms , say her last word and tell him to stop crying and look for someone new better or equal to her. I'm sure he can , he's the fastest hotty hero , girls will wait to replace Amy anytime. But with what she did for her whole life which dedicated to aiding him in his adventure or just normal everyday life , Sonic may get stuck with her death. Especially when she died from someone who intentionally kill her. He will get furious like never. Cursing those who do this to her and may be kill that bastard. At this point , what I feel is the blue is punished for what he didn't do to her. Perhaps , he shout "I love you" to lifeless body of Amy Rose.