It's caloric restriction/eating below BMR for too longs fault. And that can happen on any diet.
I've known more women who've lost their periods on CW HCLF and very low cal. I've seen women/girls doing that to themselves since I was in high school 25 years ago. I promise you none of them had ever heard of Low Carb. They were just eating extremely little in the way of food/calories.
Low carb and the satiation it provides is simply a tool that people can use to help them moderate their caloric intake, but they still need to be mindful of the effect that eating too little can have.
It distresses me to sometimes see people in the mindset that losing weight faster is better, which invariably means lower cal than they could do if they would accept a slow steady weight loss in the more normal range of 1-2 lb a week. And also the mindset that they need constant linear weight loss for large amounts of weight... say they want to lose 60lbs in 6months. Maybe they can, but it's just not a healthy goal IMO. But I've certainly seen people who push, and push, at such things with constant restriction. Or even try for months and months on end to budge those last 5 vanity lbs with constant caloric restriction + increased training.
Again, not the fault of "low carb". It is completely possible to play with the carb level you eat to get both satiation and an appropriate number of calories, and abundant vegetables per day.
The fact that some people go to extremes... is just that. Some people.
Some people will go to extremes on any diet.
Low carb offers other benefits to other people for specific reasons as well, but that is not what is being discussed just here, and/or already has been(brain issues), so I'm not going to bring it up.
In case anyone is interested switching to HFLC actually helped my period become regular again after several years of it being completely random and skipping months. I also no longer have PMS when it shows up, nor cramps.
I suspect my hormones have improved quite a bit.
So there are obviously different results.