Courtney vanished from the corner of Grand Vue and Milky Way, Salberau in Elsies River on May 4, just metres from her Pluto Street home.
Since her disappearance, police and residents have rallied daily to search for the toddler.
Speaking to Weekend Argus, Western Cape police spokesperson FC van Wyk said there were no developments. He urged people to allow them to continue with their investigation without interference.
Van Wyk also cautioned that the “finer aspects of the investigation and findings made during the police investigation cannot be disclosed”, especially to the media.
Kath Brink, founder of Little Brinks Girls, an NGO helping children throughout the Western Cape, said the organisation was concerned that many of the stories surrounding Courtney’s disappearance - including an alleged Whatsapp message sent to the family demanding a ransom for her return - were untrue.
“People in the community are coming out with the most outrageous stories and it’s heartbreaking for us and the family who are on the ground, searching,” said Brink.
“It’s becoming sensationalism all the time. It’s taking the focus off finding Courtney, and we need to find her happy and very much alive.”
Brink said it was upsetting that every lead was a “dead end”, which hampered the investigation.
“They will make up stories and keep the sensationalism going and keep the focus off Courtney, which is where it should be. We are begging the community to come forward with any valid information that can help us get her home.”
Brink said the search was continuing.
“Friday night we were searching, Saturday, Sunday. Making calls, trying to follow up leads and information. People in the community don’t know what SAPS is actually doing, how much time they are putting in, and it’s heartbreaking.”
On Thursday, more than 100 residents from in and around the Cape Flats gathered at the Peters’ Elsies River home for a prayer vigil for Courtney.
Courtney was last seen wearing a white and yellow T-shirt with blue shorts and was barefooted.