It's very typical for condom use to contribute to longer lasting erections. Because they do reduce sensation somewhat -- especially if you're not putting a little lube inside, or using the thinnest condoms -- and because the ring at the bottom of a condom also constricts the base of the penis, that's a pretty typical effect, and something some men and women consider a bonus of condom use.
It's very normal for men to reach orgasm five minutes after the start of intercourse when it continues. Overall, it takes women longer to reach orgasm than men, particularly if intercourse is all that's going on (and a majority of women -- around 70% in most studies -- won't reach orgasm from intercourse alone no matter how long it goes on for). The Kinsey Institute states that 75% of all males reach orgasm within 2 minutes of the start of intercourse. When people talk about sex going on for hours and hours, they usually are either a) talking about more than just one session of vaginal intercourse, or b) seriously fibbing.
As well, when women get really turned on by their partner's pleasure, it will tend to arouse them more and thus, get them closer to orgasm and can make reaching orgasm easier. Let's bear in mind that you're telling me that not using a condom isn't the only difference here: you also feel differently about this girl than you have other partners, and heightened emotions tend to equal heightened arousal.
You might point out that when she reaches orgasm relatively quickly, she probably isn't worried about anything: she just knows she was obviously really turned on and that whatever she was doing obviously felt really good! It certainly doesn't mean YOU aren't turned on, after all, nor that you're not interested in sex with her. It also doesn't have to mean any sex you're both having needs to end, if she really isn't finished: after all, your penis isn't the only sex organ you have, you've got hands, a mouth, a whole body to work with and that you seem to already know is enjoyable for you both.
You don't have anything to prove, and if you did, I'm not sure how your penis could prove it for you, any more than the nose on your face could prove anything. :) Being mad at yourself is pretty unproductive, and someone resenting themselves or their bodies, or feeling they have to prove something to themselves or anyone else during sex certainly isn't going to add anything fantastic to your sex life.
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