Is it permissible for me to ask my brother to waive the debt I owe him, on the grounds that I previously gifted him a similar amount when he was in need, especially after his financial circumstances have improved and he is now quickly demanding repayment of the debt?

It is permissible for the debtor to ask the creditor to drop all or part of the debt. However, if the request for the dropping of the debt is in exchange for something the creditor previously gifted, this falls under revoking a gift, which is forbidden, except for a father with his child. This is based on the Prophet, peace and blessings be upon him, who said: "The one who takes back his gift is like the one who takes back his vomit," and his saying, peace and blessings be upon him: "It is not lawful for anyone to give a gift and then take it back, except for a father concerning what he gives to his child. The example of one who gives a gift and then takes it back is like a dog that eats until it is full, then vomits, then returns and eats its vomit."