What is the ruling on a partner taking his full capital and withdrawing from a restaurant, knowing that the restaurant is still losing money and that the partner is offering to contribute to the loss but the other partners refuse?

Your partners' purchase of your share in the restaurant for an amount equal to your capital is Islamically permissible. The fact that the restaurant is losing money does not affect the validity of the transaction, as long as they both agree to buy your shares at that value, whether it is equal to, less than, or more than the original capital.