When my husband makes it for the Passover Seder, he uses the "coffee bean grinder" on our rather ancient Moulinex blender, adds a bit of vinegar, and it lasts a couple of months after Passover. I usually have some in the morning on my eggs. But that stock doesn't last forever, and the time had come for me to grind some more.
Yes, it's my job to peel and cut the horseradish root into chunks. And those chunks go into the food-processor. I use the cutting blade. And when the pieces are as small as they can get, I put them in glass jars and add vinegar. The jars then go into the refrigerator.
This should last a couple of months, and then I have to prepare more.
PS there are people who consider this condiment medicinal. It sure adds flavor.