You're focussing on the wrong thing. "About whether" is not a constituent; it's not a phrase, or a clause, or a construction. It's not anything by itself and for sure there's no rule about it. It's just two words that happen to occur together in a sentence. Both of them introduce constituents, and those constituents are stacked inside one another like Russian matryoshka.
The operative clause (the rest of the sentence is not involved) is
- there is an intense debate [about [whether [it is better to keep trying]]]
The brackets show the embedded constructions modifying debate:
- the tensed clause: it is better to keep trying (there's more clause in the original)
- the embedded question: whether it is better to keep trying, introduced by whether
- the prepositional phrase: about whether it is better to keep trying, introduced by about
Whether introduces an embedded Yes/No question
(whether is the Wh-word for Yes/No questions; it's deleted with a real question,
but retained when they're embedded).
This particular Yes/No question is
- Is it better to keep trying?
but of course an embedded question doesn't do subject-auxiliary inversion -- just the Wh-word is enough.
About is a preposition, and therefore introduces a prepositional phrase -- its object has to be a noun phrase, and embedded questions are noun phrases. Embedded questions are one of the four types of complement ("noun") clauses that function as nouns -- subject, object, prepositional object.
So in this case the preposition about takes as object a constituent clause that starts with the word whether, and that word in turn introduces another constituent clause. It's a complex situation, all right, but focussing on two words that don't belong together isn't going to help.
Look for constructions and clauses, not individual words; English sentences are not stuck together like beads on a string. They're constructed more like large buildings, with parts that fit together and support one another.