I cannot tell you how many times I hear this complaint and it saddens me to hear it.
Most of the time, not all of the time, but most of the time, the issue is that Google has penalized the site that is complaining about stolen content. Since that site is penalized, Google will rank other sites above it. Now often, those other sites have your content and are targeting your same keyword phrases and thus are ranking for the content they stole from you.
It stinks, it really does. You spend all this time and effort writing great content for your web site. It ranks well for years and makes you nice money. You participate in some link building and Google releases a Penguin update and you no longer rank well.
You then check who is ranking above you and it is your competitors, but not just any competitor, the ones that have literally ripped off your content word for word (even sometimes link by link).
They over take your rankings because Google knocked you down.
Of course, you can issue DMCA takedown requests but then the next scraper will pop up. The only solution, in many cases, is to reverse your penalty or heck, scrape your own site and start new.
Forum discussion at WebmasterWorld.