I'm trying to make what's essentially an eye bolt out of 1/4" diameter
brass rod. My first inclination was to simply heat the rod and bend it
around a mandrel. Wrong inclination. The stuff seems to get brittle
as it cools. Snapped right off. Do I have to keep the heat (MAP gas
torch) on it while bending it? Should I try to anneal sufficient
length on the rod and bend it cold?

I don't know what kind of brass this is, just whatever the local
hardware store carries. I cold bent a hook in one piece but it was a
much larger radius than what I'm trying to do this time.