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The context is nothing of special: two girls are talking about a magician that in the past was famous and well renowned, but not anymore in the present days.
One of them tell to the other one:
一時期、世間でもてはやされてはいました。しかし彼女の魔法が長く通用するはずもなかった
Maybe is (from shikashi, because the previous part it's clear):
"But was only a matter of time before her magic lose interest among the people. (the audience).
"長く通用する" is clear (Adv+Suru Vrb), it's about "はずもなかった" that I have perplexities.
Thk U in advance.
I'd translate; She had been very popular for some time in the past, but her magic would not have been widely acclaimed among people for a long time.
はずもなかった implies it could have happened but it didn't happen.
So, the famous magician had the possibility/scenario to be a widely acclaimed magician, but it didn't happen.
In other way, the famous magician might have been a very popular magician, but it isn't.
はずもない is also discussed here. はずもない、はずはない、はずがない. Difference and meaning
Subjunctive mood. https://english.stackexchange.com/questions/134926/would-have-done/136965#136965
