I'm not sure that I could help you but it might give you a lead.
I experienced the same problem a few months ago. I assumed that the battery's life came to it's end and I replaced the battery but the issue kept going. A few weeks later I realized that a lot of people were complaining about lag and battery drain on Galaxy Note (N7000). After a quick research I found out that Jelly Bean is causing this issue.
I wonder if you've updated to JB recently? If so than I could suggest to start looking for a custom ROM that could resolve this issue. I'm not saying that you should do it by any means but maybe you could take it into consideration. If you decide to proceed with flashing your phone you'll find a lot of threads in this forum about flashing custom ROMs and rooting your device.