"It was the second time it happened in as many days." - is there a description for this phrasing?

Solution 1:

As mentioned by John Lawler, this could be called a case of "coreference." Another term for it is Anaphora.

Anaphora is defined in grammar (as opposed to rhetoric) as:

use of a grammatical substitute (such as a pronoun or a pro-verb) to refer to the denotation of a preceding word or group of words; also : the relation between a grammatical substitute and its antecedent

• Merriam-Webster

This exact structure is discussed in the paper "A pragmatic analysis of so-called anaphoric islands" in the journal Language. They call this particular case of anaphora unique because "second" and "two" are not morphologically related. In that sense, it could be argued that it is a form of weak anaphora, as pointed out in LBaker's answer. However, the authors here argue that it is still appropriate, or at least, "not infelicitous."

Lakoff & Ross proposed the following three degrees of deviance for outbound anaphora:

a. if the lexical item and the antecedent are not morphologically related

...

However, it is not the case that morphological unrelatedness necessarily results in infelicitous outbound anaphora. Consider the example in 10, where the containing word second is clearly not morphologically related to the intended antecedent two.

(10) This is the second time in as many weeks.