"Please God bring him back to home," Sandra da Silva posted.
Another woman, Monique Hansen, posted in the Temuka Community Group page.
"Yes, some of you will say he is 17 and this is what 17 year olds do, he will be hiding, he doesn't want to be found blah blah blah but that doesn't mean its ok and we all just give up and stop spreading the word that he is STILL MISSING after a whole week," she said.
"His family want answers, they deserve them. Put yourselves in their shoes."
Santana's parents told Fairfax their lived had "just stopped" since their son went missing.
"We're not living, until we find him. We are desperate, we need people to help," Rosie Santana said.
"I know he knows how much we love him, and how much we care for him. We're worried about him."
The family was originally from Brazil and had lived in New Zealand for nine years.
Santana's mother said he had been quiet the last morning she saw him.
"He was walking back and forth, and then he was [seated] on the sofa, and was having toast with Marmite."
She asked where he was going as he put on shoes and socks.
"He said, 'I am just going for a walk'. He walked away to the door and didn't come back."
Santana has dark hair, is 182cm tall and of medium build.
He was last seen wearing light blue shorts and a light grey zip-up jacket, similar to the one in the supplied photo.
His top has half a zip and has light green stripes on the sleeves.
Police had been searching buildings and sheds near the farm where the Santana family lived early this week, as well as searching for the teen by helicopter, Fairfax reported.
Officer in charge, Sergeant Mike van der Heyden of Temuka, said it was possible he had hitch-hiked out of the area.
Police believed Santana did not want to be found, he said.
Anyone who sees Santana or has information on his whereabouts should dial 111 or Crimestoppers, which can be done anonymously by calling 0800 555 111.
