"He has provided the vision Facebook needed to build [the company up] to these heights and they will need him to continue to guide them," Moorhead said. "Zuckerberg needs to keep the top spot for right now to give Facebook a chance. Remember, the issues at hand are the repercussions from a flawed IPO, not a flawed company."

Karsten Weide, an analyst with IDC, said there's no way she sees Zuckerberg making way for a new business leader at the company he founded.

"Mark Zuckerberg is not going to step down any time soon," she said. "He is a man on a mission, wanting to force the world, if need be, to more openness. And as a man on a mission, he does not primarily care about business."

It's business that Stoltmann is concerned with, even though he said it is too early to throw a flag on Facebook's IPO at this early date.

"You have to give any company, especially a young company, time to mature in the market," he said. "We are all impressed with short-term movements of the stock price, but you have to give it a year or two before you start crucifying the company."