My NIV commentary indicates that 1 Corinthians 7:12-16 was written of married persons, of cases where one subsequently becomes a Christian. I assume the same standard would apply for believers who get married, where one subsequently loses faith in God. Is this correct? Are there any writings of the early church fathers which address the latter situation?
I believe you are correct. It is possible to insist that a lapsed believer is still (somehow) a believer, but this goes against the normal sense of the word believer nearly every time it appears in the New Testament. Believers are not just giving mental assent; they are living the life. If a Christian's spouse gives up the faith, in short, he or she qualifies as an unbeliever. (And yes, this certainly has significant implications in the marriage/divorce arena.)
As for the Church Fathers, I would be hesitant to accept their testimony as authoritative for Christians: Most of them are writing 4-10 generations after apostolic times. While I don't doubt that these thinkers and writers were genuine believers, I do not accept that their writings are binding for us. They were doing their best to protect the church from false doctrines, and many of the stands they took are reasonable, considering the situation, but that does not mean they were always faithful interpreters of the apostolic teaching.
The Church Fathers often wrote in reaction to Gnosticism, the more popular version of which taught that celibacy was the ideal state of a human being, even a married one. (See 1 Timothy 4!) Teaching born of reaction often falls into errors of overreaction. The pendulum swings too far.
But yes, to answer your last question, there are many Patristic passages touching on the subject about which you are asking. If you want to continue your study, you will want to access the collection of Ante-Nicene writings (the post-apostolic writings before the Council of Nicea in 325 AD). Fortunately, the many thick volumes of the series have an index, and you will find what you want quickly. Or take advantage of David Berçot's Dictionary of Early Christian Beliefs, which has culled many patristic texts on a variety of topics. This 700+ page book, published by Hendrickson, is worth what you will pay for it! The answers are there for those who are willing to dig.