Is the husband obligated to pay the deferred dower to his wife if the reason for the divorce is the wife's inability to engage in sexual intercourse due to an illness, given that they both agree to the divorce?

The deferred dowry is a right of the wife that is not waived except with her consent. It is included in the generality of Allah Almighty's saying: "And give women their dowries as a free gift. But if they are pleased to give up to you anything of it, then consume it with wholesome enjoyment." Divorce should not be resorted to unless its benefit outweighs the harm, for every illness has a cure. If treatment is not possible and you both see the benefit in separation, then there is no harm.