Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
2- Your responsibility is to exert all possible efforts to remind your wife of Allah and to strengthen her faith.
3- You have be patient with her.
4- Ask Allah in your prayers to guide her to the straight path.
Answering your question, Dr. Mohammad S. Alrahawan, Associate Professor at the department of Islamic Studies in English, Al-Azhar University, Egypt, states:
This is a test from Allah. Allah has tested some Prophets through their wives. Your responsibility is to exert all possible efforts to remind your wife of Allah and to strengthen her faith.
This may happen by asking Allah in your prayers to guide her to the straight path and by consistently advising her.
She might have been exposed to some circumstances or bad experience which affected her commitment and dedication. She might have been raised in a corrupt environment.
In case you both have children, they may be greatly affected by your separation. This is the reason you have to take all possible means for getting her closer to Allah expecting reward from Him.
My advice is to be patient with her, but if you have strong feeling she will affect your religion you may, then, divorce her.
Allah Almighty knows best.