SAN FRANCISCO -- More than a month after

Apple

(AAPL) - Get Report

CEO Steve Jobs appeared at the company's annual developer conference looking rather gaunt, speculation around his health refuses to wane.

Apple has remained tight-lipped, but analysts and portfolio managers say the chatter has become a major overhang on the company's shares.

And while some on Wall Street have maintained that Apple could have been more forthcoming and offered timely updates regarding Jobs' health, other analysts say Apple may have made the right choice in steadfastly refusing comment.

"They are being cautious, because once they start giving updates, it will become a monthly question -- and something Apple will have to deal with all the time," says Darren Chervitz, director of research at Jacob Internet Fund. The fund holds shares of Apple in its portfolio.

A virtual "Steve Jobs Health Watch" could end up distracting investors even more from the company's performance and its products, while contributing to an outsized focus on the importance of Jobs' role in the company's future -- something that Apple would like to keep in check, say some company watchers.

Apple shares fell nearly 10% on Tuesday after the company reported its third-quarter results Monday. The decline was attributed to a

weak guidance

as well as concerns around Jobs' health.

The company's stock was up $2.60, or 1.6%, to $164.52 Wednesday, but are trading about 18% below their 52-week high.

Apple, some would say, has brought some of this attention to Jobs upon itself: When concerns about the CEO's health were raised last month, Apple finally issued a statement saying Jobs' was battling a "common bug."

But now the

New York Times

reports,

citing sources close to Jobs, that he may have undergone a surgical procedure to address a "problem" that was contributing to his weight loss.

Despite the unofficial disclosures to the media, the company isn't saying anything on the record. "Steve loves Apple. He serves as the CEO at the pleasure of the board and has no plans to leave Apple. Steve's health is a private matter," Apple CFO Peter Oppenheimer said Monday in response to a pointed analyst question.

But the decision to not offer more information has left the field open to conjecture, say analysts.

"While the topic is delicate, we believe the absence of a straightforward denial of health issues will increase speculation of a worst case scenario," said Chris Whitmore, an analyst with Deutsche Bank, in a research note Tuesday.

Despite the larger-than-life personalities of their founders, few technology companies, including

Oracle

(ORCL) - Get Report

,

Google

(GOOG) - Get Report

and even

Microsoft

(MSFT) - Get Report

have seen the identity of their founder so tightly tied in investor minds to the company's future.

Because of that, Apple should be more forthcoming, agrees one portfolio manager who didn't want to be named, but whose fund holds shares of Apple. "People are concerned about Steve Jobs' health, and Apple hasn't done anything to address whether it should be a concern," he said. "Whether his health is a private matter or not is debatable, but because of his position there is no denying it is of interest to shareholders."

Barring any new information, the speculation surrounding Jobs' health is likely to continue contributing to weighing down the stock -- at least until Jobs makes his next appearance.