Investors always like to see dividend stocks with high yields. Yet looming behind those attractive yield numbers, you'll often find concerns that could result in an eventual dividend cut. To help you avoid getting involved in a company's stock at what could turn out to be the worst possible time, let's look more closely at three high-yielding dividend stocks that could face some challenges in the near future with potential consequences for their ability to keep their payouts high.

Image: Coach.

Coach could leave investors holding the bag
Luxury handbag retailer Coach (TPR -0.47%) has done an impressive job of treating shareholders well, boosting its dividend from just $0.075 per share as recently as early 2010 to four and a half times that amount currently. Yet after four consecutive years of increases from 2010 to 2013, Coach has remained stuck at its current payout level for more than two years now, and a falling share price has helped send its yield all the way up to 4.6%.

Coach's concerns have stemmed from a huge decline in its revenue, with the company's most recent quarterly results including a 12% drop in sales that slashed net income by 85%. With comparable-store sales down 19% from the year-ago quarter, Coach has investors worried that further declines could be on the way. The drop in net income has sent the percentage of earnings that Coach is using to pay dividends soaring, and that could eventually pressure the retailer to reduce its lucrative quarterly dividend. Without a turnaround in the near future, dividend investors could face some tough decisions about Coach's prospects both fundamentally and for paying income to shareholders.

BP isn't feeling energetic
The energy industry has struggled under the weight of rock-bottom oil prices, and earnings have fallen dramatically. At BP (BP 1.02%), which currently yields almost 8%, big impairment-related hits have sent the oil giant's bottom line plunging, and analysts now expect the company's earnings in 2015 and 2016 to fall short of what it has paid out in dividends over the past year.

Image: BP.

BP does have ample cash flow to cover a dividend even if earnings remain subdued. Yet the real question for BP is whether oil prices recover in the near future or remain at current low levels for an extended period. The longer that oil stays below the $50 per barrel mark, the harder it will be for BP and many of its energy peers to keep payouts at current levels. The decline in BP's share price shows the skepticism that many investors have about the sustainability of the dividend over the long run.

GlaxoSmithKline could come down with the dividend flu
Pharmaceutical companies rely on healthy pipelines of new treatments to keep their sales climbing, and GlaxoSmithKline (GSK 0.22%) has had to deal with some setbacks, with the company facing a patent cliff for one of its key medications and a relative lack of potential blockbuster drug candidates in its late-stage pipeline. Further out, Glaxo has plenty of promising drugs in development to treat a variety of maladies ranging from cancer to malaria.

For dividend investors, Glaxo has already given the bad news that it is freezing its payments through 2017. That might not sound so bad for a stock already yielding 6%, but some are concerned that unless it can turn itself around in short order, a dividend reduction for the pharma company could be in the offing. Moreover, with Glaxo having chosen not to make an expected payout of a special dividend related to its deal with a competing drug company, dividend investors are rightly concerned about whether they can trust Glaxo to do right by them.

Dividend investors need to remember that high yields always require a further look at what's behind them. In these three cases, investors should keep in mind the risk of possible dividend cuts in the future and take that risk into account in making a final investing decision.