My mac won't stay asleep

I have a noisy external hard drive, and I keep noticing disk activity. Figuring that out is another project, but I got tired of listening to it, so I keep putting my mac in to sleep mode (apple menu, sleep). It doesn't stay asleep. After a while (10 minutes? I didn't time it). I start hearing the disk going again, and if I touch the keyboard, and the machine it immediately ready. Why isn't it staying asleep? How can I make it stay asleep?