Refeeding is something that primarily occurs with people who are not in a position to lose weight (e.g. no excess body fat). If you are not in this camp, don’t trouble yourself.
Those with uteruses tend to take on quite a bit of water weight during their cycle. This too is likely the answer.
If you are feeling okay to continue physically, do so knowing that you are losing weight. How in the world do you think your body is running? It must be using body fat. The issue you’re having is you think the scale is a perfect representation of how much you “weigh”.
You shouldn’t really weigh before or during a period because your body holds onto fluid.
I fasted two days before my period. Weighed the day of my period and no weight loss.
Two days later, I was suddenly 4.6kg down.
Just keep going and you’ll eventually lose weight. You might need some potassium if you are overconsuming on sodium. As long as you are still feeling good and does not have an elevated heart rate for an extended time, just keep going.