Although fruit can no longer grow once it is picked, it continues for

Let's quickly slash-and-burn the original sentence to make this a little easier:

Although fruit can no longer grow once it is picked, it continues for some time to respire, taking in oxygen and giving off carbon dioxide, similar to the way human beings breathe.

[Fruit] continues for some time to respire, similar to the way human beings breathe.

"Similar" is an adjective, so "similar to the way human beings breathe" must describe a noun that exists in the sentence (as mentioned by other users, this is also necessary for parallelism within the comparison). So what noun does it describe? "Some time"? "Fruit"? No! It should describe "the way fruit respires", but that's not a noun in this sentence. It can't describe the verb "to respire", so there is no logical referent for "similar to the way human beings breathe". A cannot be the answer.

Taking the slash-and-burned sentence and plugging in E:

[Fruit] continues for some time to respire, just as human beings do when they breathe.

Helper verbs like "to be" (is, are, was, were, will be, have been, etc.) and "to do" (does, do, did, will do, have done, etc.) imply other verbs, but again, those other verbs must exist in the sentence. A lot of confusion regarding whether or not "do" implies "respire" or "continue to respire", but it just doesn't matter — they both create reasonable meanings:

[Fruit] continues for some time to respire, just as human beings do [respire] when they breathe.
[Fruit] continues for some time to respire, just as human beings do [continue to respire] when they breathe.

Either way, a logical sentence where "as" (a word that compares two parallel verbs) compares two parallel verbs! Moral of the story, check your referents, and don't get hung up on things where you aren't sure of the rule — there's a decent chance it doesn't matter.