I did not look at the link very closely but I surmise this is part of a discussion on whether ら抜き言葉 make the language more ambiguous and whether this could really matter in certain situations. I would read the extract as
「られる」は私の父が信じていたほどには効能を持っていなかったのではなかろうか。
Perhaps the "rareru" construction was not as efficacious as my father thought.
As per the other answer, のではなかろうか basically has the same meaning as のではないだろうか. When translating such sentence endings I think the trick is:
(1) recognise what is just a variation in grammatical style,
(2) confirm whether the writer is asserting or denying the topic using the context and
(3) when it comes to choosing the best English, there is no right answer so go with what fits the passage best but make reference to where the sentence ending lies on the "I think/Probably" spectrum of other possible sentence endings:
〜だろう
〜と思う
〜のではないか
〜のではないだろうか
I find expressions containing words like 効能 unsatisfying to translate. "Effective" was my first choice but its appropriateness might depend on exactly what the father said. I chose "efficacious" because the following definition includes all the qualities that I imagine the father believed in:
Efficacious: (typically of something inanimate or abstract) successful in producing a desired or intended result; effective (New Oxford American Dictionary)