i am the same way you describe your girlfriend. pressuring her and obsessing about it will only make her feel like she's inadequate sexually. this is not about you, your penis, or your techniques as a lover. it's her body and her sexual response. if she's happy, let it go. your issues are all about your sense of sexual prowess, and you've got to let those go. if she says she's happy with you, she is. if you can't take it that she may never have multiple orgasms with you, move on.
i have to say, i've been made to feel inadequate by both men and women because i don't have multiple orgasms-- whether they are sexual partners or not. in our highly sexualized world, it's not enough anymore to be satisfied sexually, you have to fit whatever current mold seems to be in style and right now being multiply orgasmic as a woman is part of that. i'm beginning to learn that i'm happy with my sex life, and it's no one else's business, not even my partner's, to expect me to conform what my body and mind are capable of to feed their sense of vanity.
with that said, i'm never averse to continuing so that my partner can get off or whatever, but trying to make me have multiples only stresses both of us out.