Yeah it's probably pretty normal, I wouldn't have thought to such an extent though...I don't mean to be disrespectful towards her, but it seems a bit of an insult to you that she doesn't feel comfortable with you seeing her body, especially since you've been together so long.
I guess you just have to be reassuring to her, obviously getting annoyed is not going to make her feel any better. Maybe pay special attention to the places she's embarassed about like, will she not let you go down on her? Maybe you could have a night where you don't actually have sex, but just focus on giving her pleasure, make it clear that you enjoy it and insist that you want to make her feel good (except, in less of a sleazy way than that). I mean, if she enjoys you touch then she can't complain can she? Even if she feels uncomfortable to start with she'll realise that it's something nice and maybe slowly she'll accept it?