Why, when it comes to sex and promiscuity in particular, is a woman's self-respect called into question?

It's the "Madonna or Whore" complex. It speaks to a societal mindset, (if you will) that aimed/aims to control women by linking their social status to their sexual activities.

This mind set has been in place since before recorded history in one form or another and so the origins of this mind set are hard to discern and speculate on but it is employed by both genders to their own ends and it is sad. In my opinion the term promiscuous has been bandied about far to freely. What is or is not normal, healthy sexual activity on the part of women is yet to be determined due to it having been repressed and slandered for so long. Men suffer as well from the negative societal mind sets surrounding sex, it is not just a "woman" issue contrary to the popular belief of some.

Sexual equality and sexual acceptance is difficult due to all of the negative perceptions and connotations applied to sex. Attempting to control another via their sexuality is sad and harmful. Yet we do it and sometimes the way we do it is so subtle and so engrained in our society we don't even realize that we are doing it. Until we can all accept that sex is a perfectly natural and beautiful expression of ourselves as human beings we will continue inflict pain and more often than not we will inflict it on those we purport to love the most.

Because there's gender inequality. Women who are promiscuous are always called "sluts" or "whores." For men, they're stuts!
We should stop using these terms.

Possibly but it shall be equally applied to male and female.