There's always more that can be said, but you may be interested in my response to How did fainting in the Victorian era become so gendered? What social conventions led to the loss of consciousness to be so strongly identified with women?:

To a certain extent, this may be biological - even today, it's noted in medical studies that women have a higher tendency to pass out. "Fainting, emancipation and the ‘weak and sensitive’ sex" (van Dijk and Weiling) in the Journal of Physiology, 2009 sifts through a number of physiological differences between men and women that could play a part but ultimately makes no definite conclusion on the matter.

However, the use of losing consciousness in fiction isn't necessarily an accurate representation of how often women fainted in real life. In 18th century sentimental novels, female characters often lose consciousness due to the overwhelming feelings produced by stressful events as an authorial tool to a) keep the heroine from being able to leave the situation or protect herself and b) demonstrate her sensibility (that is, sensitivity to emotion). In Richardson's Pamela, for instance, Pamela faints repeatedly when being assaulted, which shows her horror at premarital sex - laudable to the intended audience - and also gives her assaulter/future husband Mr B a chance to show his respect by not raping her while she's passed out. You have to look at 19th century fiction in context as the bearer of this legacy rather than just depicting the reality of syncope. (Also consider the comedic trope in modern-day fiction of people fainting when surprised.) Writers also made a significant number of references to women deliberately pretending to faint/be ill in order to gain sympathy or have the appearance of delicate sensibilities.

This bled into real life, in the case of women giving testimony about crimes perpetrated against them in court. A victim of rape had to have been continually fighting throughout the act for the court to convict a man in Victorian England (which many thought would make the rape impossible to achieve anyway) - or she had to have fainted when attacked and then raped while senseless. Victims in court frequently related that they had struggled to the point of exhaustion and then fell unconscious in order to satisfy both elements. Women who had been assaulted but managed to get away before being raped also described themselves as fainting afterwards, without apparently having struggled to the point of exhaustion. Fainting was essentially a part of the narrative built by the victim/defense, not necessarily consciously, to prove that they were the right kind of women.

I'm sorry that I've kind of hit at your question from the side, which I didn't realize I was doing until it was done. In terms of popular perception, it seems to come back to the sentimental novels/novels of sensibility of the second half of the 18th century. Both male and female characters in them could have sensibility and faint, but most frequently the focus was on the swooning of the heroine, which made losing consciousness an admirable show of delicacy, and delicacy was an important aspect of middle- and upper-class Victorian womanhood.

I don't believe corsets have much to do with it. I'm not aware of any studies that actually prove a link between corsetry and fainting, even after dancing or exercise, and my personal experimentation doesn't bear it out.

Further reading:

"She Fell Senseless on His Corpse": The Woman of Feeling and the Sentimental Swoon in Eighteenth-Century Fiction, Ildiko Csengei, Cambridge University

Faint or Feint?: Literary Portrayals of Female Swooning in the Eighteenth Century, Boram Kim

The Culture of Sensibility: Sex and Society in Eighteenth-Century Britain, G. J. Barker-Benfield (1992)

‘Under Cross-Examination She Fainted’: Sexual Crime and Swooning in the Victorian Courtroom, Victoria Bates, The Journal of Victorian Culture (2016)