How long can a CEO be absent before questions arise? In the case of Google (GOOG) CEO Larry Page, the answer is about a month.

Page wasn't at the Google shareholder meeting Thursday because he lost his voice, the company said. OK, that's understandable. But he won't be participating in the company's earnings call either, which is weeks away. Why is he skipping out on the call?

JP Morgan analyst Doug Anmuth also noted that Page hasn't posted on the Google+ social network since May 25. Kinda hard to sell your social network if the CEO goes for nearly a month without posting anything. Page will also be absent next week from Google's conference for its Android software.

"We have no specific reason to think there is anything more to Larry's condition, but we find it odd that the company would already rule him out of the 2Q call which is likely still a few weeks away," Anmuth wrote in his note to investors, according to Cnet. "We think this could raise some questions among investors."

It's not uncommon for CEOs to take some time off from the public eye, and Page has many initiatives to juggle at Google. But what is unusual is for Page to miss so many high-profile events -- particularly the shareholder meeting and the quarterly earnings announcement.

Are shareholders worried? Google's stock price has fallen about 2% since Tuesday. Hard to tell if that's directly related to Page, though.

The best thing Page can do is make some sort of public appearance -- even if it's just updating his forgotten Google+ page -- to put these questions to rest. As the public face of the company, it is his job to assure shareholders that all is well.

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