Explanation
Correct answer: C.
Choice C is the best answer. The convention being tested is the use of punctuation and verb forms within a sentence. This choice leaves the verb "admired" in its nonfinite past participle form to function within a supplementary element ("much…followed"). Offset by commas after "works" and "followed," this supplementary element interrupts the main clause ("English poet and Shakespeare contemporary John Donne’s works…had…been essentially gathering dust…") with additional information about the works’ reception during Donne’s lifetime.
Why the other choices are wrong
Choice A
Choice A is incorrect because it makes “were much admired during his lifetime and in the decades that followed” a finite predicate, then places “had been essentially gathering dust” after a comma without a conjunction. The two predicates cannot be joined this way.
Choice B
Choice B is incorrect because using the finite verb "were much admired" results in an ungrammatical sentence.
Choice D
Choice D is incorrect because “had been much admired during his lifetime and in the decades that followed” is already a finite predicate, and the sentence then adds “had been essentially gathering dust” after a comma without a conjunction. The two predicates cannot be joined this way.