I've only really had 2 instances of needing to Fear RP, on two seperate personas.
The first was snaga-napped, when that was still a think, and I screamed and yelled until their throat became hoarse. Admittedly, he was a snage all of about an hour before being rescued, but I played him with a constant underlying fear of it happening again.
The second was my Wood Elf, who's brash at the best of times. I played her as more violently threatening than scared as that would be her reaction, to try and mask the fear with a brave face. Didn't play out too well, but also Krug was easy to escape then and she lead low. To this day though, she's not entering a cave unless there's a damn good reason to.
Fear RP is hard, for the reasons mentioned above by others, but in my situations death wasn't too much of a risk so I was free to have fun with it. I think part of the problem is that death is usually the only outcome in situations. I can't tell you the number of times a persona has been mugged on the way somewhere, surrendered their stuff, then just been killed for the hell of it. Even a fresh persona I made once asked someone for some food, and then got killed. If death is the only outcome, who's gonna bother RPing the fear when it's 'just another death'?