Translation:It was while Grandmother was still alive.
That's not an accepted word order. Swedish wants the fortfarande before the verb here (but adverbs are tricky, sorry).
In that case, why is "min kusin levde fortfarande" the target answer for one of the other questions in this topic?
Adverbs will generally prefer to come after the verb in a main clause. But they will generally switch places to come before the verb in a subclause.
Det var [=main clause] medan farmor fortfarande levde [=subclause].