I face the same problem from time to time and explored some options which might be useful to you as well.
Here are some possible reasons and solutions. Search engines keep the pages in cache. First scenario: Your page is not indexed soon after publication, meanwhile some one else copies it and gets it indexed earlier than you. Then the algorithm wrongly thinks some other page as original.
The best way to avoid is to bookmark/ ping/tweet/fb your pages soon after you publish. This helps in building related pages and also helpful in indexing soon. (This is not to build back links to your page, which is a different matter). However one should not over do this as again it may look spammy. In my opinion a couple of book marks at prominent sites will do.
Second scenario: Your page is established but for some other reasons got penalized (by Google in this case). Then G may push it to far end and bring some copy of it (for the same kw) to the forefront. In this case you need to analyze the cause and rectify it if possible.
It may also help if you contact the owners of copied pages and tell them to remove the copy. In one such case of mine, the guy was kind enough to remove the copied page immediately (the meaning of kindness got degraded so much :))
If they don't do, you may have to send a copyright violation notice, however I have never done this. Registering your page at free copyright sites helps in establishing your page ownership in time, for future usage if required.
Hope this helps.