Apple investors should be some of the happiest shareholders on Wall Street. And for the most part, they are. But when it comes to the question of dividends, the gratitude vanishes.

Year after year, Apple (NASDAQ:AAPL) investors ask about a dividend. Year after year, Apple declines to offer one, rewarding shareholders instead with handsome returns in its stock value. Apple returned investors more than 25% in 2011, a year when the rest of the market basically flat-lined.

Now, investors and analysts have gone from asking about a dividend to predicting that Apple will pay one in 2012. An analyst from ISI Group went on CNBC to declare that an Apple dividend “is going to happen.” Earlier, a fund manager at Gamco Investors made a similar claim. Even IAC‘s (NASDAQ:IACI) Barry Diller disparaged the concept of growth companies not having to pay dividends as “outdated and somewhat inane.”

Nevermind that Apple last paid out a dividend 17 years ago, when Michael Spindler was CEO. Or that Steve Jobs – who made tens of millions of dollars a year from Disney (NYSE:DIS) dividends – never felt a need for one, preferring to have large piles of cash as a safeguard that allowed Apple to take risks.

Now that Jobs is no longer involved, investors are cranking up their expectations that a dividend to come. After all, Apple’s cash pile keeps growing – from $40 billion a year ago to $80 billion today. And analysts figure free cash flow will keep adding $40 billion a year for the next couple of years. And besides, Apple’s stock, valued at a moderate 15 times earnings, could get a boost by the increased demand that a dividend would create in the stock.

Apple’s new CEO Tim Cook is clearly facing pressure to pay a dividend. He mentioned in a recent conference call with analysts that he’s “not religious” about holding or not holding cash. Some read into his words a softer stance on the dividend issue, but the language is as vague and noncommittal as Jobs’s old comments on Apple’s cash.

In time, Apple may capitulate to investor demands, but that time isn’t likely to come in 2012. Here are some reasons why.

In Silicon Valley, dividends are a sign you’re over the hill. They’re what you pay to mollify investors who want to know why growth is slowing. But Apple’s revenue is expected to rise 29% this year with earnings increasing by 25%. Microsoft (NASDAQ:MSFT) pays dividends. Google (NASDAQ:GOOG) doesn’t. And Apple doesn’t want to be seen as losing face before its rivals.

Apple is also seen in the tech industry as the world’s largest startup. True, this “startup” has a $388 billion market cap, but Apple is regarded as the prime example of a tech giant that can still innovate like a scrappy newcomer. Startups view cash the way Jobs did – as a cushion to protect you when risks don’t pay off. Handing it to investors signals to software developers everywhere that you’re losing your edge.

In fact, for all of Silicon Valley’s materialism, it also has a strong current of idealism that Apple embodied under Jobs. Cook’s Apple is keen on preserving the ideals of its longtime CEO, so a dividend so soon after Jobs’s death would look like a step away from those ideals.

In addition, most of Apple’s cash is overseas. Like Google and Cisco (NASDAQ:CSCO), Apple invests much of its profits in countries with lower tax rates. To pay a dividend, Apple would need to repatriate cash and also pay a U.S. corporate tax rate closer to 35%. If the U.S. grants a tax holiday, Apple may give in and pay a dividend. But a tax holiday looks unlikely in 2012.

The calls for an Apple dividend aren’t likely to go away, and in fact will increase as the company’s cash pile grows. But the simple reality is that tech investors need an Apple dividend much more than Apple needs to pay one. The kind of reliable growth that Apple delivers regularly is hard to come by, even in the tech sector.

Few investors are foolish enough to punish Apple by selling their shares. And that leaves complaining as their only option.