Mr Davidson said it was believed Thames may have scented another group before becoming separated from his handler in dense bush.
It was hoped Thames would head downhill, following a river or a track, Mr Davidson said.
Search teams, including Thames' handler, spent Sunday night in the bush, hoping he might respond to calls or be found near one of the main tracks.
Thames' handler intended to remain in the bush until his dog was found, Mr Davidson said.
"The handler has built an affinity with the dog - it lives with him and his family. They spend every working minute with each other - it's a huge bond."
"He will be feeling it, very, very badly."
Each police dog costs between $40,000 to $60,000 to train and they were an invaluable resource "worth a heck of a lot to us", Mr Davidson said.
Thames has been an operational police dog since 2012.
Local farmers and others living near the Mt Holdsworth access roads were asked, along with trampers and outdoor enthusiasts, to keep an eye out for Thames.
Anyone with information was asked to contact the Wellington police district command centre on 04 496 3473.