I have been noticing, however, that my hair seems to be thinner or, should I say, some of it has been falling out.
Hair loss is one sign of malnutrition.
You did not state your weight and height, but I suspect that your rate of weight loss is too much. Also, the diet you are on may be lacking in protein, vitamins or minerals, but mostly likely it is just too low in calories. If you are eating 1000 calories a day or less, for a period of 4 months, you are undernourished. You are at risk of losing muscle mass along with the body fat. Your hair loss is evidence of that.