The Wiki page on Fear Reapers didn't have this:
Is there a max range on the Fear of Death effect? Was in The Pit, had a Fear Reaper spawn at the top of the first furnace by the Elly. Had me dotted up pretty good before I could see it. A bit of trial & error showed me I couldn't lose his agro/effect no matter the distance I tried to escape - even way down at the bottom I got more stacks.
First time I've run into one in such a large environment, anybody have some helpful range info?