"Rabbits have a lot of offspring."
Translation:Kunikloj havas multe da idoj.
It's the object of "da", which does not take the accusative.
"Kunikloj" cannot have an object, as it is not a verb. "Havas" can have an object, which is "multe da idoj".
Because the accusative only applies to the direct object of the verb, and that's limited to adjectives and nouns.
multe is an adverb and
idoj is the object of the preposition