Wow, that would make sense if that was the problem ("Most of devices are charged even if you turn off your computer unless you plug out the power, but sony reader is not.")
I also don't think the sony readers are the right answer for PDF files - they will do the job just not perfect. My ipad is much better. I don't do PDFs, especially DRMd, on the sony. I stick with epub and have had no problems with files or battery life. We charge 1x a week but that is because hubby likes all 4 bars, not 3.