Jumping the Shark: definition 3 according to the Urban Dictionary.com website:
"...the point when a television series shows it has run out of ideas and must resort to stunts to retain viewer interest. Derived from a scene in the last years of Happy Days when the Fonz waterskied over a shark."
"Jumping the shark is an idiom created by Jon Hein that was used to describe the moment in the evolution of a television show when it begins a decline in quality that is beyond recovery, which is usually a particular scene, episode, or aspect of a show in which the writers use some type of "gimmick" in a desperate attempt to keep viewers' interest."
Clever readers will be quick to point out that Happy Days lasted for years after this scene. This observation is true, but off point. The "stunt"/"gimmick" parts of the definitions are what count here. As the last several years have demonstrated, the writers for Doctor Who are hardly out of ideas, so changing the Doctor's gender -- an inexplicable desire on the part of a minority of "fans", that raises it's head everytime the character has a regeneration pending -- is simply that, a gimmick. It serves no narrative purpose in the revived series, or in the broader context of the show's half-a-century history; it does nothing to enhance, flesh-out or otherwise actualize a character that -- apparently surprising to some -- has continued to develop and grow as portrayed by "white" males from the U.K.
I know there are some hardcore arguments for the sex-change like: "It's about time", "the show's about change" and my favorite: invoking the throw away line about the Doctor's Time Lord friend, the Corsair, in the 2011 "series 6" episode: The Doctor's Wife, about how he/she regenerated into a woman a couple times. It's a sign of our times I think, that this, coupled with his/her ritual tattooing of the ouroboros on every one of his/her regenerations, doesn't indicate the Corsair may have had some unresolved mental or emotional issues... And we know, for Time Lords, this sort of thing can be brought on as early as the age of 8. Remember what happened to the Master when he looked into the "untempered schism"? Well, he didn't become a girl, anyway.
Demonstrating "the female Doctor" as gimmick and nothing more is simple. How? We'll take the statement: "The next Doctor could be a woman!", and play with it.
"The Next Doctor could be blind!" Comedic and dramatic gold here! Not a lot of advocates though. Not as "sexy" or as part of the current cultural focus is it? Being blind...
"The next Doctor could have six arms!" He's an alien, right? The show is "about change" goes the online chorus, correct? Romana regenerated into a blue midget on a whim. (See Destiny of the Daleks). Eccelston's Doctor did imply he could have two heads after regenerating in the Parting of Ways... but that was a throw-away line to ease Rose into the idea of him regenerating. The Corsair thing, THAT was meaningful!
"The next Doctor could be a chain smoker!" THIS I personally would like to see. If you faced what the Doctor faced on a regular basis, you'd be lighting up too.
"The Next Doctor could be Pixar animation!" Omg...that would be like selling Star Wars to Dis... never mind.
And on and on ad absurdum. (Actually, a few of those ideas are WAY better than a sex change for the Doctor...)
Now, my own personal take on the Doctor's ability to regenerate is also simple. He sucks at it.
So over the course of 50 years of show time and 750+ years of onscreen Time Lord lifespan, (assuming Hartnell's Doctor was around 500) the Doctor has "died" from old age, forced regeneration, radiation poisoning, being mashed to bits from a fall, blood poisoning, physical trauma, gun shot wounds followed by exploratory surgery, eating the time vortex energy, and radiation poisoning again... and none of those triggered his mythical estrogen reservoir to make his man parts go away in favor of being a female.
Here's another problem. Why the disrespect to women? Seriously. Why do they have to be used parasitically to alter an established, firmly male character and even spark a debate like this? Don't they rate their own hero? Are there no more Xena's, Buffy's, Lara Croft's, Scully's, Ripley's, Sailor Moons, She-Ra's, Kim Possible's, Bat Girl/Oracle's, Sarah Connor's Princess Leia's etc. in writers' imaginations? You can't tell me the Doctor needs a sensitivity make-over. He's more than made up for that in the last 8 years. He should grow and evolve as the Gallifreyan man he is and always has been. (Potentially with a human mother, but that's another debate over a throw away line)
There are plenty more stories and generations of writers to tackle further Doctor adventures, don't throw away the show on a gimmick or "just because".