For those of you who -- like me -- haven't watched the entirety of the Doctor Who series: This is the scene I'm referencing here. Take the time to watch it. It happens to be pretty cool.
Maybe I hadn't seen a connection to IM3 if I hadn't read about the pseudo-empowerment of Pepper Potts before. (I can't find the article anymore but it was pretty good.) In any way, Anita Sarkeesian notices this phenomenon as an aside in her 2nd episode of "Tropes vs. Women in Video Games" as an essentially meaningless Power-Up of characters otherwise firmly rooted in the Damsel in Distress trope.
Dr. Who's Rose Tyler's purpose in the series is mainly ogling the Doctor, being jealous and getting herself into trouble for the Doctor to rescue her. But in this wonderful episode, she actually develops a fleeting glimpse of agency and actually does good. However, the amazing powers she harnesses from having looked into the TARDIS are too much for her frail human mind and the Doctor has to -- surprise, surprise -- save her by sacrificing one of his lives.
In Iron Man 3, Pepper Potts does not even decide to take action herself. Tony puts the Iron Man Suit on her to save her from an explosion and she just happens to wear it for a couple of minutes until Tony needs it back. The other time, she's genetically mutated by the Bad Guy and thus is turned into a glowing goddess. Seriously: Other people are ripped apart by the procedure, but Pepper handles it like a boss. Although she kicks some major ass when mutated, the movie does not even as much as question Tony's decision to "heal" her from that "affliction".
These characters get their superpowers from an outside source which isn't all that special in and of itself: Most superheroes gain their powers by the (metaphorical) radioactive spider-bite or have to labour in order to build the gadgets like the Iron Man Suit. Other than their male counterparts, however, these powers are shown as dangerous and even lethal in women, so it's up to the male hero to save them from them. An accept-and-master-narrative that is so typical to superhero stories does not take place.
Maybe the "I looked into the TARDIS"-Syndrome is not limited to female characters but is really a trope of minor characters. Iron Man 2, however, would point to a gender-based trope. Can you think of any male characters suffering from this?