Thomas Chu, an experienced open water diver, was last seen Sunday removing his weight belt as a strong undertow swept him away from other divers near Race Rock, southwest of Victoria.
A search by military aircraft and coast guard vessels was called off Monday but his grieving family hopes it will resume.
Chu's brother Joshua says the Search and Rescue Society of BC resumed a shoreline search Thursday but gale warnings and high waves prevented the use of underwater sonar.
The family started an online petition urging resumption of a full-scale search, and it has already gathered nearly 9,000 signatures.
Chu's family says he was serving as a Metropolitan Police special constable in the British capital, was about to begin training as a lawyer, and a guild in London honoured him as Soldier of the Year in 2011.
Also on HuffPost