Sometimes God allows what he hates to accomplish what he loves.
Love is extravagant in the price it is willing to pay, the time it is willing to give, the hardships it is willing to endure, and the strength it is willing to spend. Love never thinks in terms of "how little," but always in terms of "how much." Love gives, love knows, and love lasts.
Alzheimer's disease is never an 'accident' in a marriage. It falls under the purview of God's sovereignty. In the case of someone with Alzheimer's, this means God's unconditional and sacrificial love has an opportunity to be even more gloriously displayed in a life together.