Perception matters. Right now he is perceived as dodging the question. He can turn that around in an instant, yet he declines every opportunity to do so. Cruz’s problems are caused by Cruz.
Actually, he can't turn it around in an instant. Regardless of the answer he gives or the strength of the denial, he's in no better position than the situation of responding to "have you stopped beating your wife". Anything he says would make his situation worse. The correct answer is generally to move on with the campaign, unless there is evidence of whatever it is in the rumors.
Responding just puts the rumors on the front page longer, or that is the standard advice. This feeding frenzy seems more severe than most, in part because it's being fed by very active paid advocates (including several brand new FR posters) who are stirring it up on social media.