What is "Regula Fidei" and is this principle of interpretation considered obsolete by those who practice the Grammatical Historical approach to hermeneutics or does it survive in some form?
Regula Fidei is Latin and means "Rule of Faith" or "Analogy of Faith".
For a quick definition:
the rule of faith means something extrinsic to our faith, and serving as its norm or measure
In essense, it's the ultimate authority that is used to measure the faith of a given doctrine or belief.
How do we measure faith?
The entire idea of the Rule of Faith stems from this one verse:
Romans 12:6 (NIV)Emphasis added
We have different gifts, according to the grace given to each of us. If your gift is prophesying, then prophesy in accordance with your faith
It is this last phrase "in accordance with your faith" that has lead people to understand that faith can be measured.
In particular, this phrase refers to one of three possible ideas, depending on the doctrine:
Per this doctrine, the rule of faith is purely found in the Bible.
"We believe that the only rule and standard by which all dogmas and all doctors are to be weighed and judged, is nothing else but the prophetic and apostolic writings of the Old and New Testaments"
(Form. Concordiae, 1577)
Per the doctrine of "Faith alone", the ultimate authority is the type of faith that can move mountains.
Through the view of the doctrine of "Grace alone", the Rule of Faith is simply the person's belief and response to the grace of God.
These different views of the Rule of Faith are used to measure the faith of a given doctrine or belief.
Regula Fidei as a Hermeneutic Principle
Regula Fidei from a Protestant (Sola Scriptura) stance is a hermeneutic principle. It has been summed up as "Scripture interprets Scripture". However, as we see above, Regula Fidei is a bit more broad of a concept than simply "Scripture interprets Scripture" and can actually be applied as a non-hermeneutical concept.
If we limit the concept of Regula Fidei to a hermeneutic principle, however, this limits us to the Sola Scriptura understanding of the concept. In order to compare Regula Fidei to the Grammatical Historical appraoch, we have to make this limitation in understanding.
The Grammatical-Historical assumes that there is only one distinct sense to the text. The approach attempts to discover the meaning of the text as the author intended it or as the original audience would have understood it.
The goal of the Grammatical-Historical approach is to understand the history and the context of the text as well as understanding the text itself in order to discover the meaning:
The interpreter should, therefore, endeavour to take himself from the present, and to transport himself into the historical position of his author, look through his eyes, note his surroundings, feel with his heart, and catch his emotion. Herein we note the import of the term grammatico-historical interpretation.
Milton S. Terry, Biblical Hermeneutics (NY: Philips and Hunt, 1883), 231.
See also: Wikipedia
Regula Fidei vs Grammatical-Historical Approach
If we compare these two approaches, what we have is the idea that we can use scripture in order to understand scripture compared to the idea that we should take the text alone with the historical setting in order to interpret scripture.
If these are in conflict, then we must accept that that the original audience or the author would not have understood other passages as being related to the passage in question.
If these are in harmony, then we must presume that the original author/audience would have considered these other passages when the text in question was being discussed.
Ultimately, these two approaches aren't necessarily exclusive. I've heard of them used together, for example, when discussing Revelations (eg "the original audience would have understood this as a reference to this passage here").
However, it seems that these two mindsets come from different perspectives and that someone who is using a Grammatical-Historical approach isn't keeping Regula Fidei in mind (and vice versa).
Ultimately, these two concepts aren't necessarily exclusive. However, the person that is interpreting the text will probably tend to ignore one while they use the other.
Regarding survival, it seems that while both approaches have historical roots, they are both alive and well among different communities.
The rule of faith is the standard by which faith is measured. The Catholic church certainly practices the Grammatical Historical (GH) approach and their regula fidei is the Magesterium representing the church. But they do not only practice the GH approach.
For those who solely practice GH, the Chicago Statements on Biblical Inerrancy and Hermeneutics are attempts at such a rule. However, one can only rule what one can destroy. So in practice, the rule can only be applied within the bounds of recognized authority. If one cannot be excommunicated, then no rule can be enforced. It is a bit odd that Reformation theologians would attempt to form a new priesthood above the average believer who is instructed by God to study to show themselves approved.
Therein lies the tension. How can a rule of faith be enforced when your statements of faith make us a nation of priests and individually responsible for understanding and obeying the scriptures.
So the direct answer is, No. Those who practice GH alone currently believe they can enforce a rule of faith through fellowshipping and coersion, as demonstrated by the production of the Chicago statements and the political fallout in the respective denominations that adopted them.