And a band of about 30 volunteers have been putting posters up in various towns to bring people's attention to the search.
"People have got no idea of the steps we have been taking to try and find him," said Flavia, who thanked the many people who have been helping.
Each phone call regarding local sightings has been checked (there were 10 a day initially but none now), a pet detective hired, flyers printed, drone flown, social media campaign kept strong, newspapers, radio stations, councils and vet clinics contacted as well as streets, parks, properties, streams, rivers and beachlines scoured.
"It was pretty much like a fulltime job."
Three motion sensor cameras, courtesy of Huha, were used, with some of the couple's clothing, Rock's toys and some food placed nearby.
"We bought a roasted chicken each day for a couple of weeks."
They were given a dog trap from the pound, which needed to be checked every two hours including overnight.
One day Rock was sighted close to the couple's house.
"A lady rang at 1am on Friday and said she had just seen a border collie on its own in the middle of Marine Pde."
A frantic search for two hours proved fruitless.
After that they decided to bring Cris' parents Jaime and Vilna Avila over from Chile for three weeks, just before Christmas time, to help.
Rock had lived with the Avilas in Santiago, where he grew up, so it was thought their scent and voice might attract Rock.
"They tried everything to find him and were really tired after a week," Flavia said.
Rock was three months old when he was given to Cris when he was working in a rural part of Santiago.
The dog suffered a broken tail when he was a puppy when a tractor ran over it, and was lucky to survive.
But the injury has created a very distinctive identification feature as he can't move his tail which is always low and between his legs.
Flavia and Cris moved to New Zealand four years ago and Rock was reunited with them on October 10.
It was a long process getting Rock to them and involved lots of paperwork, thousands of dollars and a spell for the pooch in quarantine in Levin.
Rock, a friendly and agile dog, was enjoying his new life in Paraparaumu Beach but on November 11 the couple returned home a bit later than usual and he was gone.
They presume he got bored and jumped a fence.
Flavia and Cris have been "completely exhausted" with the search but vow to continue.
"We have to keep going and spreading the word around," Flavia said.
"It has been very hard but we can't stop thinking about him."
If you have any information about Rock call 021 139 4790.
