Search continues for missing fashion house CEO

Vittorio Missoni is photographed at the Missoni trunk show at Neiman Marcus Beverly Hills, October 20, 2011.
David Crotty/ via AP Images

(CBS News) Venezuelan crews continued the search on Monday for the CEO of Missoni, one of the largest fashion houses in the world, after his plane went missing last week.

Vittorio Missoni was last seen returning from vacation with his wife and four others on a small plane that disappeared off the coast of Venezuela Jan. 4.

Can Missoni survive disappearance of CEO?

The BN-2 Islander plane took off from Los Roques, a string off islands off the coast of Venezuela, at approximately 11:30 a.m. It was scheduled to land 42 minutes later at an airport outside of Caracas, but never made contact with the control tower.

Missoni is the eldest son of the fashion house's founder, Octavio Missoni, and is widely credited with making the name a global brand.

Over the weekend, Missoni's son took to Twitter, writing, "Please help us find my father."

His sister Angela told an Italian newspaper that the family remains hopeful about the outcome of the search.

However, CBS transportation safety analyst Mark Rosenker explained that, "the longer that the search and rescue operation continues, the chances of a good outcome are really diminished."

Venezeula's government said it will not call off the search until the plane is found.