Hi Mack! I haven't personally experienced hair loss as a vegan (I have been vegan since early 2011). I have very very thick hair though I keep it short. I DID lose some hair when I suffered with anorexia nervosa and was at my lowest weight and restricting hard (I was an omnivore at that time). In fact it was the worst when I was several months into recovery and eating way more. I learned that hair health is more reflective of your health several months ago than at present. Eating too little for an extended period and/or rapid weight loss can cause hair loss, but usually there are other symptoms that go along with that.
At any rate, my Mom went vegan for a while several years ago. She has a gluten intolerance so has eaten gluten free for years, and she has bad bouts of diverticulitis, several times ending up in the ER, so she can not eat seeds or nuts. She also has a huge bias against soy. And she is in her 70s. So with all those restrictions in mind and her age etc, several months into her being vegan she visibly lost a ton of hair. It was actually quite alarming. Her iron and hemoglobin tested fine so it was not that. I suspected it was lack of omega 3 fatty acids due to her not eating nuts/seeds or soy, and she didn't eat a ton of leafy greens (I personally eat about three to four cups a day of them). Her hair loss stopped and began to reverse somewhat when she started eating fish again. I tried to get her to start taking vegan DHA/EPA supplements and flax oil so she has been doing that and weaning down on the fish and so far so good. I do know that I have gone through periods of extreme low fat eating and my hair, nails, and skin just don't fare as well as when I include a few servings of healthy fats in my diet each day. I'm not a fan of oil, but I do incorporate flaxseeds, chia seeds, pumpkin seeds, sunflower seeds, almonds, cashews, walnuts, avocado, coconut etc. My average fat intake percentage per day is still only about 15% give or take but it seems to work for me.
Also, do you consume beans each day? They are an excellent source of many nutrients.
Finally, have you had your thyroid checked? I have hypothyroidism (for 26 years now) and certainly when it was very low I had bouts of hair loss.