What is the ruling regarding a husband who divorced his wife while she was menstruating, then divorced her with an irrevocable divorce, and then took her back with a new marriage contract?

The correct view is that divorce during menstruation is valid, and the divorce becomes irrevocable (bain) if it occurs before consummation, or upon the expiry of the waiting period (iddah) following the first or second divorce without reconciliation. Irrevocability also applies when the wife chooses separation through the option of irrevocable divorce, or when the ruler divorces the wife. In these cases, the husband can remarry his wife with a new contract and dowry, unless it is the third divorce, in which case she is not lawful for him until she marries another man. Based on the question, the first divorce occurred during menstruation and the second was irrevocable. The husband is permitted to take his wife back with a new contract and a new dowry, if she agrees.