For example (the twins are mentioned as possible subjects….): “their” refers to the twins.

More troubling is the meaning of “maintained their innocence”. Maintain may mean “hold on to” or “continue to assert”, but in the latter case, it should be followed by a finite clause, not a noun phrase. So “maintain their innocence” can’t mean “assert that they are innocent” but must mean “hold on to their innocence”.

So the sentence is grammatically correct (although there’s a typo in “throughout”) in a context such as

(The twins’ older sister may have been brutally raped but) the couple has maintained their innocence throughout the ordeal.

“couple have maintained its” – 0

“couple has maintained its” – 0

“couple have maintained their” – 10

“couple has maintained their” – 14

The last combination occurs in several distinct articles, so it’s not just a case of repetition. The source of the first article is AP, which is known for rather high journalistic standards, including spelling, so they have my full confidence.

The word “their” has been used correctly because it is referring to the couple as a whole. Unless of course the couple changed their point of view and where their innocence would be past tense, has would be then be changed to had.

Also, (although this may have only been a ‘typo’ on your part,) the spelling of ‘throughout’ is incorrect.

has is singular

their is plural

It needs to be either:

“The couple have maintained their…”

(the couple treated as two people – my preferred option)

or

“The couple has maintained its…”

(the couple treated as a single entity)

throughtout

should be

throughout