Hank is right. You are probably using too much pressure for those finer grits. I would also recommend with the final couple of grits, it helps to sand with the grain, after sanding with the lathe on. Just some manual sanding with the grain, light to moderate pressure (enough to do the job, but not so much as to burnish or anything like that.) Look for spots where the grain may have been torn by lower grits, try to clean those areas up, get the blank as consistent as possible all the way around.
I have sanded at a wide range of RPMs...from 1000 up to nearly 4000. With the right pressure (not too much), you shouldn't have problems with the wood burning or burnishing. I usually try to sand at around 2000-2500 rpm these days, though, maybe even lower with larger pens (larger diameter, especially caps...maybe 1800).
Approach sanding as a delicate process...not a rough or heavy handed process. This is your finish...the final process. Approach it with care, and a measured hand. Attend to the wood, or the acrylic, and work out the rough spots carefully, meticulously.