I had a much worse problem. I was lucky if I would get your worst case scenario I was getting more than 10 wrong in some passages. I am now consistently getting no worse than 22/27 for a section thanks to the Memory Method:

http://classic.7sage.com/lesson/the-memory-method-for-improving-lsat-reading-comprehension/

I'm not sure if it's included in all of the courses but follow JYs instructions (yes do the writing on a separate piece of paper, yes get extra RC sections if needed to just drill passages). I noticed significant improvement after a couple days of just drilling using this method.