Pepper gets really pissed off when people dismiss Tony because the media portrays him as either a two-dimensional arrogant asshole, or a tortured bad-boy sex god. Yes, he always comes off initially as a charmingly self-absorbed carefree idiot, and yes, he sleeps with a lot of women, and yes, he's so self-absorbed that it takes him ten years to remember a birthday, but there's so much more to Tony than that flat caricature of a man. Those characteristics are Tony, but Tony isn't those characteristics. Tony is a man who, on any given day, will put his own life in danger to save hundreds, maybe thousands of others. Tony is a man who, in his spare time, will develop technology twenty years ahead of its time out of table scraps and attic scrapple. Tony is a man who, when given the chance, will give a ludicrous sum of money to any group he thinks is doing something worthwhile. But, no matter how amazing Pepper thinks he is, she knows better than to make him aware of it – his ego is already the size of the sun, there's no reason to inflate it anymore.
After Afghanistan, Tony doesn't sleep around. He still flirts outrageously and isn't above fully utilizing his stripper-plane, but it's kind of hard to set time aside for sex when he spends his nights recuperating from super-villain attacks, or halfway to the Middle East, or fishing out bullets from his suit, or improving his suit, or fixing his suit, et cetera. It takes a little while for his friends to notice, but they're too afraid of touching anything related to Afghanistan to really pursue it. Besides, if they bring it up Tony might take it as an invitation to hold public orgies in his house or something.
In the early years of her employment Pepper knows, even objectively, that Tony is really incredibly rakishly handsome. But, however attractive he may be, she herself has never seen the appeal of his 'bad boy' charms, which was what made her the idea PA – she was the most efficient person Tony would listen to (as much as Tony would listen to anyone) and the person most immune to his charms and able to put up with his bullshit. She sees firsthand how he treats his one-night stands, and while he is generous and accommodating, it's most definitely not what she wants in a relationship. It's only after Afghanistan that she actually lets herself fall for him, and only because of the potential he has, because the inherent goodness that's always overshadowed by his sleazy playboy antics and his absurdly hedonistic lifestyle is finally coming to the surface.
Tony has never seen his proclivity towards sleeping around as amoral – he gives all his ladies a good time, and he never gives them any impression that this is more than a one night stand. It's not his fault if sometimes there's the occasional girl with the harebrained scheme of changing him, of commitment, of turning their hilariously short 'relationship' into something meaningful. While he actively tries to avoid these types, there's always that one hysterical dame that always gives Pepper a little trouble in the morning. Of course many people disagree with this mentality (including Pepper), but his flippancy eventually deters them. However, while he does enjoy a good chase and while he is rather persistent, Tony will never force himself on anyone. If a girl is entirely disinterested and does not succumb to his charms in the slightest, Tony may be intrigued and may test her a bit (or a lot), but ultimately he will back off because while he may be a self-professed bastard, he's not that much of a scumbag. Besides, there are hundreds, maybe thousands of girls who would willingly sleep with him – why make too much fuss about one that won't? He may occasionally act like a spoiled child, but give him some credit.
Pepper Potts has actually thought of quitting several times – there is only so much genius-billionaire-playboy-philanthropist malarkey someone can handle before snapping. Cleaning up after one too many one-night stands, covering his ass for one too many scandals, being responsible for one too many executive meetings and corporate decisions that are all supposed to be his responsibility seems like more trouble than it's worth on some days. But then he always does something so thoughtlessly thoughtful that indicates that yes, Tony Stark is more than just snark and smartass asides. One time he made her clear his schedule so he could spend the day building a prosthetic for some kid in Connecticut, a runner who was relying on his legs to get him a full ride to college; there was a tractor accident, and his family couldn't even think of being able to afford any kind of replacement until Tony stepped in. Another time he personally funded the renovations for a public school somewhere in New York about two months from being shut-down and condemned. She doesn't know how he finds these stories but before they're over he always finds some way to fit himself in and rewrite the ending, and for all the attention-seeking self-centered stunts he pulls, these are genuine. He always gets agitated when congratulated for something he thinks should be considered common decency. And so she stays, because there's something worth staying for. Because he's worth staying for.
(It doesn't hurt that he's prone to giving her ludicrous bonuses when he acknowledges the bullshit she puts up with. Say what you will about Tony, but there are times when he's an excellent boss.)
Contrary to popular belief, Tony Stark is not a misogynist. While his default reaction to a woman is to flirt outrageously, he doesn't see them as having an inferior intellectual capacity - that's how he sees the majority of people around him. It comes with being a genius, especially an impatient one: everyone around him is slow on the uptake, and no one can ever keep up (except Pepper, and even then she tends to slip behind). He has a hard time talking to people because he doesn't dumb things down for anyone, it never occurs to him, and then he gets frustrated because nobody understands him. His reputation as one only exists because it tends to be more fun to sleep with women than to sleep with men. What Tony respects in a person is competence and intelligence, and with the acute lack of either in the majority of the human race, especially at his standards, Tony doesn't really see the point in making the pool of truly capable people even smaller by eliminating specific demographics.
(He was actually pretty surprised that there was any negative reaction to Pepper's accent to CEO just because she was a woman – he's seen firsthand what she's capable of, and honestly she'd probably run rings around all the competitors if given the chance.)
The first time someone insinuated that Pepper's primary job was prostituting herself to Tony, she slapped the egotistical asshole and stormed out of whatever fancy shindig Tony was attending. It was also the first time Tony had to handle PR for anything she'd done, and he handled it surprisingly well. The third time she denied it until she was red in the face, stating all her qualifications and all of the jobs she's required to do for Mr. Stark, and finishing by daring the nosey reporter to repeat what she just said. The ninth time she stopped him at "I heard that you…" and called her boss over, making something up about how her conversational partner was just about to bring up stocks and how Stark Enterprises fit into their future. She probably took too much enjoyment from how much Mr. Vice President of Whatever Corporation squirmed as he hastily backpedaled. The twenty-eighth time she just gave a look and a cold, thin-lipped smile as she described exactly thirty-seven ways she could ruin the gossip's company.
The first time someone called Pepper a whore to Tony's face, he laughs it off and countered with an estimation of how many women he sleeps with per week. "Now why would I need to pay someone to have sex with me if I could get your date to drop her panties in, oh, maybe five seconds flat if I tried?" He winks and saunters off, finding the whole thing almost hilarious. The seventh time, he responds with a barrage of casual insults, while vocalizing several interesting facts about the offender's budgetary analysis of the fiscal year, and how quite a bit of money seemed to just disappear, now isn't that odd? The eighteenth time, he buys out the company just to be able to personally fire the stupid ponce for some fabricated misdemeanor, and the thirty-second time, Tony just punches the bastard so hard he flips over the bar.
So there was this seven-hour drive in China and I got bored. I'm not quite sure if this actually counts as fanfiction, but oh weeelllll.