Steve Jobs, CEO of Apple (AAPL), has announced that he will be relinquishing his day-to-day duties, taking a “medical leave” from the company. In Jobs’s absence, COO Tim Cook will manage the day-to-day operations of Apple, the manufacturer of the popular iPhone and iPod devices. “I have great confidence that Tim and the rest of the executive management team will do a terrific job executing the exciting plans we have in place for 2011. I love Apple so much and hope to be back as soon as I can,” said Jobs in a statement.

This is the second medical leave taken by Jobs, as he underwent a liver transplant in 2008 and was away from work for six months. Jobs’s health problems began in 2004, when he was diagnosed with pancreatic cancer and underwent surgery to remove a cancerous tumour. Jobs’s pending leave of absence has led to a decline in the stock price of Apple, as their share price declined from 344.99 to 326.72 in the period between Jan. 14, and Jan. 21.

Despite Jobs’s high profile and reputation as a visionary leader, Apple should remain on course in his absence. COO Tim Cook has previously managed the company during Jobs’s previous leaves of absence, and the company remained stable and profitable during that time. Though in the short term Jobs’s absences have caused declines in the share price of Apple, in the long run the trend has stabilized and disruption to the company was minimal, though perhaps only because of Jobs’s eventual return.

This is just the latest in the speculation and concern about Jobs’s health, according to BBC News technology correspondent Rory Cellan-Jones. “There is no other technology firm — probably no other major business — whose shape and direction is so much in the hands of one man as Apple. Steve Jobs is not only the public face of the company, at the launches of new devices like the iPad, he is involved in every minute detail of Apple products. So for the last half dozen years every hint, every rumour about his health has sent shockwaves through the investment community and caused Apple’s share price to plummet.”

It is impossible to predict with certainty what will happen if Jobs is unable to return to the full-time management of Apple. He has become so closely associated with the company, and is such a hands-on leader, that his absence could leave shoes that cannot be filled. Apple has succeeded in large part because of Jobs’s ability to push the company in new directions, to take risks and to stay on course through difficult times.

David Garrity of GVA Research remains bullish on Apple’s prospects, despite admitting the importance of Jobs to the company: “Jobs is seen as being intertwined . . . and his presence has meant a great deal to investors and consumers at large,” Garrity said. “We may also get some further announcements coming out of the company as to what they intend to do with $50 billion worth of cash. [Apple] could initiate a dividend and could have a buyback — and still be in a situation where they continue generating cash on the balance sheet this year.” Apple’s $50 billion cash pile comes from larger than expected profits, as well as their reluctance to use additional funds to acquire other companies, or return the money to their shareholders as dividends.

Whether Apple’s future will be as strong as its recent past may depend on whether they can maintain their innovative culture, and remain one step ahead of their competitors. With Jobs’s remaining as CEO, and a reliable man in charge of day-to-day operations, Apple’s competitors would be wise not to underestimate them.