The group filed papers with the Western Cape High Court in an attempt to stop the channel from airing pornographic material from 1 December.
The Independent Communications Authority of SA (Icasa) granted the pay channel permission in April to air three adult content channels: Playboy TV, Desire TV, and Private Spice.
Icasa stated that the channels could only broadcast adult content between 20:00 and 05:00.
"As advised by counsel, [we] believe that Icasa erred in law in failing to find that the constitutional rights of children were laws of general application, which should have trumped the rights of Top TV to freedom of expression," Jasa director John Smyth QC said in a statement.
"[We] contend that fixing a watershed time of 20:00 flies in the face of common sense, bearing in mind that most teenage children finish their homework at about 20:00 and then watch TV for an hour or two until bedtime."
Jasa has asked that the court review the Icasa findings and send the matter back to Icasa for it to apply the law correctly.
"We don't think they [pornographic programmes] should be broadcast at all, but after 23:00 would be a more reasonable time," said Smyth.