grammatical number - Is "leave of absence" a countable noun?

Normally, if a word is generally uncountable ("English vocabulary"), but sometimes it becomes countable to convey particularity or variety ("the many vocabularies of various English dialects"), it'll be labeled as [U, C] in the Oxford Advanced Learner's Dictionary, or as [uncountable or countable] in the Longman Dictionary of Contemporary English. The noun leave is, thus, only uncountable, as it's only labeled as [U] and [uncountable]. I even consulted Wiktionary, and it's still labeled as uncountable, with no plural form given. And yet, this Wikipedia page employs a host of singular and plural forms of leave of absence.

So could leave of absence ever be countable and take a singular form as a leave of absence and a plural form as leaves of absence?

Answer

Yes, the noun phrase leave of absence is countable, with the plural being leaves of absence. This is confirmed by the following dictionary example, despite the entry marking the head noun leave as a mass noun.

leave noun2 (mass noun)
1 Time when one has permission to be absent from work or from duty in the armed forces.
‘Full-time officers of research may take leaves of absence according to the policies described below.’
- ODO

Suppose one goes on leave for medical reasons, and upon the period's expiry takes personal leave, they are on leave (non-count) for the whole duration. They aren't on (*) two leaves. Likewise, if another person takes some time off as well, we still say that the two people are on leave (still non-count). It's non-count because it refers to a state of their employment. There is no change to the state even if multiple episodes are ganged together.

Since on leave refers to state, it doesn't become plural even when talking about separate, non-consecutive episodes. One says that someone has been on leave twice, not that they have been on (*) two leaves.

However, a leave of absence is understood as a defined episode:

A leave of absence (LOA) is a period of time that one must be away from one's primary job, while maintaining the status of employee. This contrasts with normal periods away from the workplace, such as vacations, holidays, hiatuses, sabbaticals, and "working from home" programs, in that they are considered exceptional circumstances, rather than benefits. Generally such an arrangement has a predefined termination at a particular date or after a certain event has occurred.
- wikipedia

Because these episodes can be counted, the term leave of absence is treated as countable.

(*) The asterisk is a convention that ELU uses to flag instances of non-grammatical usage.