The Portland Trail Blazers haven't had a six-game losing streak since their dismal 2005-2006 campaign, when the team finished 21-61, with an 11-game losing streak and four (!) separate six-game losing streaks along the way.
In 2006-2007, the longest losing streak was five games. In 2007-2008, the longest losing streak was five games (on three separate occasions). In 2008-2009, the longest losing streak was three games. In 2009-2010, the longest losing streak was three games.
This chart is a quick look at the Western Conference playoff teams from the last five years. The teams are listed in seed order, accompanied by their regular season win totals and their longest losing streaks of the year.
As you can see, there wasn't a single Western Conference team that suffered a six-game losing streak and still qualified for the playoffs in either of the last two seasons.
But, in 2007-2008, both the Utah Jazz and Houston Rockets made it to the playoffs with six-game losing streaks. In 2006-2007, the weakest overall year for the conference during the past five seasons, the Los Angeles Lakers qualified with a seven-game losing streak and the Golden State Warriors qualified with a six-game losing streak.
In total, that makes four times in the past four seasons that Western Conference teams have qualified for the playoffs after enduring a six-game slide.
As for Portland and the playoffs this season? On the bright side, teams have been where Portland is right now and survived to make the post-season before. So this isn't unchartered water and the playoffs aren't yet an impossible dream. But it doesn't happen very often, especially when the conference is deep with talented teams, as it presumably is again this season.
Despite their ongoing six-game slide, the Blazers are currently tied with the Warriors for 9th place in the Western Conference with a record of 8-11, two games behind the Phoenix Suns, who are the No. 8 seed. (As of this writing.)
All numbers courtesy of Basketball-Reference.com.