Honestly, I have no idea, as I never tried that. Although I had large printouts, and it seems the oldest ones are lost, IIRC.
But for such long-running logs, you should use a real logger. For a primitive one (just appending given text to a text file), you can look at my e-mail sketch, which uses a simple logger. I added it to test logging after exporting to an application: that's another reason to use logs to text. Beside, once you get a text, you can use the search capabilities of your favorite text editor, etc.
Another advantage is that if your computer or your program stops working, you still have the log...
http://bazaar.launchpad.net/~philho/+junk/Processing/files/head:/_SmallPrograms/Email/