I've never had a problem with it burning, since most stabilized woods are fairly soft to begin with. I usually take it to 600 grit, hand sanding, then buff with white compound until it looks like a mirror. Some of the very soft woods need to be sanded to a finer grit before polishing to avoid undercutting.
Yeah, I don't think Desert Ironwood is "stabilized" except by nature maybe. One giveaway is that it certainly DOES burn if you don't use fresh belts. Hard stuff!