"Are Polar Bears in Decline? Greenpeace and the Natural Resources Defense Council initially presented only one academic study that found polar bears are currently in jeopardy. The study examined one population of polar bears in Canada’s Western Hudson Bay, where the average weight of female polar bears fell, leading to reduced cub survival. It linked the early break up of seasonal ice in the bay to a 21 percent decline in that polar bear population.

However, Alaska’s polar bear population is stable, and research by Mitchell Taylor, a biologist with the Nunavut Territory government in Canada, shows that the Canadian polar bear population has increased 25 percent during the past decade, from 12,000 to 15,000. Where polar bear weight and numbers are declining, Taylor thinks that it is due to too many bears competing for food rather than Arctic warming."
http://www.ncpa.org/pub/ba/ba610/

Now, keep in mind that this study has do with Hudson Bay, and it is typical that all [or least most] of this Hudson Bay sea ice melts every year- the most northern part of Hudson Bay is hundreds of miles south of the Arctic Circle.

As far as I can tell this is that one study:
"We analyzed data for polar bears captured from 1984 to 2004 along the western coast of Hudson Bay and in the community of Churchill, Manitoba, Canada. The Western Hudson Bay polar bear population declined from 1,194 (95% CI = 1,020–1,368) in 1987 to 935 (95% CI = 794–1,076) in 2004."
http://www.bioone.org/perlserv/?request=get-abstract&doi=10.2193%2F2006-180&ct=1

So, most likely it is a measured decline of about 259 polar bears, though due to possible [unlikely] errors in the survey the polar bear population reduction could have been more severe than this or remained unchanged to slightly increased.
Now, a possible reason for such a study, is that citizens may have been complaining about increasing numbers of polar bear in places where humans were living. As later in report it mentions:
"It may also explain why Churchill, like other communities along the western coast of Hudson Bay, has experienced an increase in human–polar bear interactions in recent years. Earlier sea ice breakup may have resulted in a larger number of nutritionally stressed polar bears, which are encroaching on human habitations in search of supplemental food. Because western Hudson Bay is near the southern limit of the species' range, our findings may foreshadow the demographic responses and management challenges that more northerly polar bear populations will experience if climatic warming in the Arctic continues as projected."

Now, as mentioned these polar bears live about as far south as polar bear live. And if they lived 200 miles further north, they would still be about a thousand miles from the Arctic Circle. And polar bears in this region have never experience sea ice that is present year round. And what does the town of Churchhill call itself "the polar bear capital of the world". Well they do have a train that can get you there, and they have an airport which serves a hub to travel further northward.
http://www.townofchurchill.ca/cim/75C122_207T4906T278T8353T413T16705.dhtm

So, the survey basically attempts to prove that polar bear population were not increasing and claimed that because of global warming these bears were eating human garbage instead seals. I don't know if the study actually proves anything other than there doesn't appear to a problem with over population of bears and people should probably avoid killing a lot of them. Meanwhile, the general trend is that polar bear populations are growing in the Alaska region and remaining about the same in Canada's arctic region.

It should also indicate that since polar bears live in a region where the sea melts completely- if the polar ice were to completely melt each summer, the polar bears are quite capable of living in such an environment. Of course I don't see any cause to make think that all the polar ice will ever completely melt anytime within the next century or so- and beyond this timeframe a coming ice age is just as likely as any other scenario.

Some other data about sea ice in Hudson Bay:
"Gagnon and Gough next turned their attention to complementary data, which resulted in mixed signals of climate change depending on the variable, time period, and location. In analyzing regional air temperature across the Hudson Bay region they conclude that temperatures changed over the second half of 20th century in much the same pattern as has been portrayed for the greater Northern Hemisphere: a peak in warming during the 1950s, followed by cooling in the 1960s and into the 1970s, and a renewed warming over the last couple of decades."
http://www.worldclimatereport.com/index.php/2007/01/15/more-arctic-contradiction/

And some Hudson bay sea ice graphs:

And the focus of following picture is arctic ice, but one can also see Hudson bay:

and 2005: