You just need her to be honest with you.
Truth be told, I don't really enjoy oral - and if I felt like I *had* to orgasm in order to show my OH that I enjoy it when we do it, I'd feel so pressured I'd stop wanting it all together.
If she only likes oral a little bit or finds it difficult to orgasm from it then she needs to learn (and for you to understand too) that orgasms aren't the important part of sex and she can have oral for as long or as little as she likes as long as she enjoys it. If it's not her favourite thing it can be a stepping stone to other forms of sex but I suspect if she feels comfortable about opening up to you on her reasons then she may enjoy it enough to let you indulge her once in a while. But she still may never love it and that's ok too.
I don't really like oral because I find it hard to switch off and added pressure of proving my enjoyment to the OH would just kill it completely for me so she needs to know you don't mind how much she enjoys it because you're completely confident that she loves your sex life together anyway!
The sensitivity thing could be a factor - I'm over sensitive so oral can be a completely different situation as I feel tense and prepared to react to sudden "catching" of a sore or sensitive bit.
You just need her to understand that:
1) orgasms don't matter
and
2) her enjoyment is important to so you'd appreciate her being honest and telling you what she likes so you can focus on the things she likes.
Hopefully she can open up and explain why she dislikes oral and maybe try it again with no pressure for her to love it or orgasm!
Adx