By Yereth Rosen

ANCHORAGE, Alaska (Reuters) - The family of a man who mysteriously vanished during a fabled Alaska mountain race last week has apparently given up hope of finding him alive and will hold a memorial service this week.

Michael LeMaitre, a 66-year-old Anchorage resident, failed to finish the July 4 Mount Marathon Race in Seward. His family ran an obituary in the Anchorage Daily News on Thursday and has scheduled a memorial service for Friday evening.

No trace of LeMaitre has been found despite an extensive search of the area around the steep, scree-strewn course, which measures just one-and-a-half miles up and back. If he has perished, he would be the first fatality in the Mount Marathon Race's 97 years as an organized competition.

Rescue workers said hopes of finding him alive had dwindled with each passing day, and the organized search effort would likely wind down at the weekend if no sign of him was found.

"Each day that goes by, the possibility goes down," said Dave Squires, chief of the Seward Fire Department.

The event, touted as one of the oldest footraces in the nation and likely the oldest mountain-running contest, is an Independence Day tradition in Alaska.

Competitors scramble up and down a steep mountain on a course that includes rocky cliffs, dense forest, loose shale and a creek bed. The most accomplished include cross-country skiers on the U.S. national team.

LeMaitre's disappearance and severe injuries to two other runners this year have prompted calls for new safety rules.

Suggestions have included helmet requirements, mandatory GPS chips for runners, as well as time cutoffs and organized trail sweeps to aid stragglers, said Cindy Clock, of the Seward Chamber of Commerce, which manages the race.

(Editing by Tim Gaynor and David Brunnstrom)