That is sad that your sister’s husband would leave her because of a mental illness.  Most wedding vows include words such as ‘in sickness and in health’, so he committed himself to stay with her regardless of any illness…physical or mental. 

If they are still together, I encourage you to encourage them to get some good Christian counseling before separating or divorcing.  You didn’t mention if they were believers, but since you wrote to a Christian site for advice, I will assume they are.  A good Christian counsellor would remind him of his vows that should last ‘until death do you part.’  Perhaps there are things she can do that would make things easier, too.  Has she seen a doctor for her mental issues?  Are there treatments or medicines that could help her with her illness?  I am not suggesting she is at fault because of her illness, but if she can get treatment that would help her control the symptoms of her illness, that could go a long way in helping their marriage survive and thrive.

With all that said, let’s look at the scriptures to find the answer to your question.  The Apostle Paul wrote in 1 Corinthians 7:10-15, “And unto the married I command, yet not I, but the Lord, Let not the wife depart from her husband: But and if she depart, let her remain unmarried, or be reconciled to her husband: and let not the husband put away his wife. But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away. And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him. For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy. But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.”  Here are the main points of this portion:

*The wife should not leave her husband.

*If she must leave, she should not remarry.

*If possible, she should seek to be reconciled with her husband.

*The husband should not make his wife leave.

*If the husband is an unbeliever, the wife should not leave him.  (While a saved person should not marry an unsaved person, sometimes one gets saved after marriage.  If the wife becomes saved after marrying an unsaved man, she should not leave him because he is not saved.)

*The unbelieving spouse (and any children) are in a special place to realize the convicting power of the Lord if the other spouse is saved.

*If the unbelieving spouse leaves, the other is ‘not under bondage’.

I believe the principle of the last point would be applicable in your sister’s case.  He may not be an unsaved man leaving to escape the constant testimony of a saved wife, but I do think the principle would apply here.  If your sister’s husband should leave her, and your sister comes to the realization that he has moved on and is not going to come back, I believe she is then ‘not under bondage.’  If he divorces her, then it is very clear that he is not coming back.  He may possibly marry someone else, leaving her alone.  In that case, she would not be under the bond of a marriage that her husband had dissolved, and she would be free to remarry “only in the Lord.”  That is, as the Lord directs and leads her and another man to become man and wife.  (374.6)