Dividend-paying stocks have been an income investor's dream for the past few years.

While bank CDs and treasury bonds have been stiffing investors with interest rates around 1%, dividend-paying stocks in the S&P 500 have been busy paying shareholders dividend yields around 2.5%. Some dividend payers like AT&T (NYSE: T) or Exelon (NYSE: EXC) have even rewarded shareholders with yields around 6%.

Big yields like that can mean big income streams. For every $10,000 you invest in stocks with a dividend yield of 6%, you can expect a quarterly dividend check of $150, totaling $600 by year's end. Invest a $100,000 to $500,000 nest egg in a basket of dividend payers like these, and you could collect dividend checks worth several thousand dollars every few months.

It's wonderful. That is, as long as it lasts.

What if all that once-reliable dividend income were to be suddenly chopped by 10%, 20% or even 50%? Or what if it stopped coming in altogether? Unfortunately for many income investors, this is increasingly becoming a stark reality.

Lethargic economic growth, depressed future earnings forecasts and post-fiscal-cliff tax hikes on dividends have pushed many more companies to cut dividend payments than in recent years. In January 2013 alone, some 44 companies announced that they will reduce the size of their future dividend payments -- some to be cut in half. That's on top of the more than 90 companies that announced dividend cuts the month before and nearly 30 companies that gave the bad news the month before that. To give you some perspective, during non-recessionary times (particularly 2004-2007 and 2010-2011), the number of companies announcing dividend cuts averaged just 10 per month.

Still, some income investors have had it far worse. After suffering heavy losses in 2012, J.C. Penney announced in January 2013 that it would stop paying its shareholders a dividend altogether after paying one for more than three decades. Those relying on J.C. Penney's 4% dividend yield saw their income stream vanish in a day.

Before you do anything in response to this trend, just relax. There's no reason to dump all of your dividend-paying investments (there are plenty of companies that still diligently pay dividends). But the possibility of a future dividend-cutting trend -- at least over the short term -- raises a legitimate question:

What should you do if you're invested in a company or mutual fund that suddenly announces that it will cut or suspend its dividend payment?

Should you sell the stock, even if it's been a great company in the past that could bounce back? Should you hold on to it if you rely on dividend income? And how can you tell if the company will announce another dividend cut in the future?

Before you decide if you should keep or dump a dividend-paying stock or mutual fund that recently cut its dividend, there's one move you must make. You must answer these three major questions:

1. Does the company have a good reason behind cutting its dividend payment?

Dividend cuts usually happen during recessions -- when companies expect their earnings to fall over the next few quarters and are strapped for extra cash. But regardless of the economy, companies can announce a dividend cut at any time for a number of reasons, some that could lead to future growth and others that could signal flailing business.

Knowing the reason a company or fund cut its dividend is essential when you're deciding whether to hold or sell, so for some expert insight, I turned to income investing expert Amy Calistri. Amy has given advice to thousands of income investors for years on the best ways to find reliable dividend-paying stocks and funds.

The first course of action, she says, is to look at the press release that originally announced the company's dividend cut and see what the company plans to do with its newly freed-up cash. Does the company plan to expand by investing in a new product line or by acquiring competitors? Does it plan to pay down its debt to strengthen its financial position? Or does it have any other growth plan that sounds reasonable to you as a shareholder?

Amy advises investors to be wary if a company offers only vague details about future plans.

'I recently sold a fund that cut its dividend -- and then didn't explain why,' she said. 'I don't invest in mysteries.'

She adds that while dividend cuts for mutual funds and stocks are mostly a bad sign, she does give them a chance on one condition: Companies and funds should articulate what isn't working and explain how they're going to fix it.

'They need to assure me that they can maintain or grow the dividend going forward,' she said. 'If they don't have a plan to do that, I'm out.'

2. Does the stock or fund still fit my investment goals?

It's one thing to know if the company is making a good decision for its future growth, but it's much more important to know if the company, as your investment, still fits your needs.

'What do you need it to do for you [as an investor]? If you own something for growth, the dividend isn't a priority. If the company continues to have a good outlook for earnings growth, you're in a position to sacrifice a little income in lieu of potential appreciation.'

For income investors, she says it’s a different story: 'If you own something for income and it stops giving you income, that's a problem, and a dividend cut is probably a bad sign for the future. It could be a great appreciation story if the company decides to invest in itself instead of paying a dividend, but that isn't what you need.'

If an investment isn't delivering what you need, you're better off selling it and moving on. Amy said she sees too many investors hold on to stocks with declining dividends with the hope it will one day restore its former rate of distribution. As Amy says, 'Hope doesn't pay the bills, dividends do. There are literally thousands of publicly traded investments. If one stops meeting your needs, find another that does.'

3. Checking under the hood -- can the company, fund or REIT afford to keep paying me a dividend?

How can you be sure that this is an investment that will keep paying dividends in the future rather than one that will leave you strapped for cash? For starters, don't rely on the press release alone -- a company's management has a way of putting a positive spin on its finances to keep investors happy. Instead, look into a company's financial health on your own.

Don't worry: You don't have to be an analyst to do this. If it's a stock that's in question, you'll want to find the company's payout ratio, which measures how much a company is taking from its earnings to pay its shareholders a dividend. You can easily find a company's payout ratio on Yahoo Finance under 'Key statistics' (here's IBM's payout ratio as an example).

The higher a company's payout ratio is, the less available cash a company has to work with to pay you a dividend. Amy cautions that 'unless you're invested in an MLP, REIT or a BDC (business development company), a payout over 80% is troublesome' as it means the company is already using 80% of its earnings and may not have much room to keep paying you that dividend if its earnings dip in the future. (I talked in more detail about the payout ratio in this article.)

Amy uses a similar method to test an income-focused, closed-end fund's dividend strength: 'In funds, I look at what portion of the dividend they've been able to cover from income.'

When it comes to investing in real estate investment trusts (REITs), Amy looks at the REIT's funds from operations (FFO). If the FFOs have been stable or growing over the past few years, it’s a good sign that the REIT's ongoing operating funds are robust enough to keep paying its shareholders future dividends. (You can see how to find an REIT's FFO here.)

The Investing Answer: As a final word to income investors looking to preserve their wealth after suffering from a dividend cut, Amy suggests looking at the company's broader picture before making any decisions: 'More than any number or ratio, I rely on the fundamental story.'

Ask yourself: Is this a company or fund that is growing or not? Is the company's industry healthy enough to lift earnings and support dividend payments in the future? What's the company's track record -- is this the second or third dividend reduction?

If things look bad for a dividend-cutting company or fund, be prepared to leave.

'There are plenty of securities that are not cutting their dividends -- and in fact are growing them,' Amy said. 'Find one of those.'