So I haven't lost my period(and fingers crossed I won't) and here's basically what I've done to make sure I don't. Before I begin note that I didn't lose an insane amount of weight, I am underweight currently but I only lost 17lbs to get there and I lost it slowly and I'm still slowing losing.
Think GBOMBS thats greens, beans, onions, mushrooms, berries, and seeds. So basically a very nutritious diet when you do eat. From what I've read on here, many people also recommend increasing your protein intake. You could try increasing fat intake as well but from what I've seen on here it may not be as important as protein. And carbs, even if you hate them, there are lots of ways to get healthy carbs.
I would also recommend vitamins/supplements if you aren't already on some. I take probiotics, prebiotics, vitamins D3 and B6 and B12, B folate, and Zinc. I'm not on this anymore but Black Kohosh (sp?) is really good for your cycle. It's also pretty cheap and may even come in a blend of other stuff good for PMS/hormones.
It is also important to make sure you are not over exercising. But be patient too bc you can lose your period after weight loss and weight gain and it can take awhile for the body to adjust