Corrections officials said they had "ongoing concerns" about Arps' risk to the public, in particular to the Muslim community, after fears over his "general behaviour" towards prison staff, along with intercepted letters and phone calls.
The content of those letters and phone conversations were suppressed by Judge Stephen O'Driscoll at a special hearing over Arps' prison release conditions at Christchurch District Court in January.
Judge O'Driscoll approved extra special release conditions, which included a ban on Arps entering or loitering near any mosque, prayer room, or any other place where the Muslim community congregates, without prior written approval from his probation officer.
The Christchurch businessman, who owns a Nazi-themed insulation company, is also not allowed to contact or associate with any Muslims without approval.
Corrections said the moves were for "victim safety" and felt that jail time hadn't reduced his risk to the Muslim community.
Arps, who does not hold a firearms licence and has more than 30 previous criminal convictions for indecent assault, guns, drugs, burglary, and fraud, is also not allowed to possess or use firearms, or to be involved in airsoft or BB gun activities.
Arps unsuccessfully challenged the extra conditions sought by Corrections in the District and High Courts.
He has now been refused leave to appeal in a higher court.
Arps submitted to the Court of Appeal that both judges in the lower jurisdictions failed to take into account the New Zealand Bill of Rights Act 1990 when approving the conditions.
But Justice Edwin Wylie refuted that.
"We do not consider that there was any discernible error in the way in which [either judge] approached the imposition of the additional release conditions sought by the Department of Corrections," he said in a decision released today.
"Both were clearly cognisant of the statutory purpose that limits the imposition of conditions... Both identified that the primary purpose of imposing the additional conditions was the need to address the increased risk of reoffending posed by Mr Arps.
"Each condition was considered in detail, to assess whether it was appropriate and whether it was phrased in a way that was reasonably necessary and proportionate to
the offending, and the risk of further offending.
"There is no basis on which it can be asserted that there was a miscarriage of justice."
Justice Wylie said Arps had not raised any "issues of general or public importance" in his appeal bid.
"There is no risk of a miscarriage of justice," he commented.
In the earlier High Court ruling Justice Rob Osborne said "very soon after the murders and other crimes of March 2019", Arps had found a way "both to trivialise and to glorify horrific crimes against a particular community".
"The fact that the killer's acts are now, by virtue of his guilty pleas, able to be formally characterised as crimes, serves to reinforce conclusions earlier reached in regard to the avoidance of further trauma to members of Christchurch's Muslim community," he said.
Justice Osborne noted that Arps appears to have a "deep-seated enmity towards people of the Muslim and Jewish faiths".
"The enmity has been manifested in vitriolic language and activity. It seemingly occupies his mind both when he is awake and asleep," he said.
It has led him into offending on two occasions in recent years.
In 2016, Arps was one of a group of men who filmed themselves doing Hitler salutes as they delivered boxes of pigs heads and offal to the Al Noor mosque.
"White power … Bring on the cull," Arps was seen saying in the video.
In that case, he was convicted of offensive behaviour and fined $800.
The second resulted in his pleading guilty to two charges of distributing objectionable publications in 2019 in the form of edited video footage of the March 15 shootings.
