At the Court of Appeal in Wellington on Tuesday, Mr Harrison argued publication of his client's name would cause extreme hardship for Senior's "fragile" 92-year-old mother.
Mr Harrison also said lifting suppression would create a risk of prejudicing a possible re-trial.
But the Court of Appeal said there was not enough evidence to uphold the appeal on either ground.
The Court of Appeal said Senior's mother's situation was "regrettable" but fell well short of the legal threshold needed to continue suppression.
The court dismissed any idea lifting suppression would prejudice a possible re-trial for Senior. Mr Harrison said his client was considering appealing his conviction, partly on the basis of claims there were issues with the credibility or reliability of some complainants.
"We agree with the Crown's submission that this second ground is entirely speculative...Mr Senior has not yet appealed against his conviction," Justice John Wild said in court. "In our view a real risk of prejudice to a fair retrial, if one were ever ordered, is not made out."
But the Court of Appeal agreed to a "period of grace" in which time Senior could tell his mum about the conviction.
Mr Harrison said it would potentially take some time to communicate the news of last Thursday's guilty verdict. The Court of Appeal heard Senior was previously incapable of bringing himself to tell his mum of the conviction.
Senior originally faced 48 counts involving 10 complainants. A jury found him not guilty on 11 counts and he was discharged him on a further two counts.
Senior is expected to be sentenced on February 20.
