Assalaamu alaikum,
(mildly) I think each person has to look at the whole situation. What is the nature of the disorder? Is it treatable? Is the person acknowledging their problem, and willing to treat it?
What is the person's underlying character? Are they kind? Are they responsible? Do they have taqwa (and by this, I mean do they sense God's Will and try to bend themselves to it, not do they spout Islam in a superficial way. Because someone could have a degree in the Islamic sciences and pray and fast… but be a deeply corrupt person who has no fear and awe of Allah).
It's also useful to look at the extended family. What are they like? Are they supportive of their loved one? Would they help you? Could they help compensate for the particular problem?
Finally, if there is any possibility of children in the equation, it is very important to ask yourself: how would this illness impact the children? For instance, you might feel you could cope with someone who gets depressed and suicidal… but it is very hard for a small child to understand this, and it is frightening. Or if, for instance, the person is emotionally unavailable, realize that this is subtly deeply damaging to a child… unless, perhaps, the extended family could help fill this need?
There will always be some flaws. You can't "have it all". On the other hand, while Muslims are supposed to restrain themselves in adversity… we are not supposed to go looking for adversity. And we are responsible for what kind of parent we provide for our children (if we have/ are able to have any).
(smile) Each person is unique. And each situation is different. There are no cut and dried answers. (smile) And this is the challenge and beauty of this life: we must think, we must reason, we must listen to our hearts… and we must make choices. Many choices over our lives. Always trying to ascertain what is Pleasing to God in esch instance, and then choosing that option.
May Allah, the One Who Fashioned us, Help us to struggle to do His Will… and become that which only He Knows we can be.