Technically they are in the consumable category. However, they can be sharpened numerous times before they need to be discarded. They're in the same category as end mills. They too can be sharpened a number of times before they are no longer useable.
Dozens of companies sell drill sharpening equipment. Cheap grinders can be purchased for less than a couple hundred dollars while top of the line equipment goes for several thousand dollars. Personally, I sharpen all letter drills, fractionals down to 1/16" and number drills to #60. In years past I was sharpening 50 or more drills a month. I wore out a Drill Doctor and replaced it with a Black Diamond model 65 drill grinder.
As a kid I worked at a GM assembly plant. One of the jobs I had was to drill the front fenders of Chevy and GMC trucks for the bolt on chrome moldings and trim. They sharpened bits down to the point that there was only one complete circular flute remaining. I'm guessing each bit was sharpened several hundred times before being discarded.
Here are a few pictures of my Black Diamond drill grinder. It usually takes less than a minute to sharpen a dull bit. A little longer if the tip is chipped or it needs to be a split point. It can sharpen any angle from 80 to 140 degrees.
