Martin Leslie has turned down the Edinburgh Gunners' offer of a short-term contract during the Six Nations championship.
The Gunners will be without new Scotland assistant coach Todd Blackadder during the tournament and he could miss seven Celtic league games.
Edinburgh chief executive Jim McKenzie said, "It is a huge disappointment to us.
"Martin explained that he has become quite caught up with a new career in the building industry in New Zealand, which he didn't expect, and feels he cannot now leave that to come back to us."
"We will continue looking, but obviously it is difficult to find an experienced, quality player available at this time of the year, so we may turn to the clubs for help again and look to see if there is a good, young forward coming through who would like the chance to step up," McKenzie told The Scotsman