I never washed my rope, but:
1) I store it in a pop-up bin IKEA-like, both at the crag and at home, so it picks up very little dust
2) When lowering off I always grab the braking end of the rope with a cloth, thus I somehow clean it in the process and avoid burning my hand by accident (I stopped using my Petzl leather gloves... another story)
Yes, I do look like a freak at the crag, but my Sterling Velocity is like new after two years of use and abuse!