The only quest I have ever died in (so far) is Monkey Madness. In fact, I died twice while trying to do it!
The first time, I was in that temple place withthe lvl 167 monkey guards. The 3 next to the trap door are unable to walk through, and I was stupid enough to get stuck in the middle with all 3 monkeys attacking me. I couldn't walk anywhere, and I couldn't kill them! Every time I got their health down to a certain point, they gained it right back. AND I didn't have any teleprt runes.

So I realized I was dead, and turned Protect From Melee off.
The second time, when I was going to fight the demon, I equipped the 10th squad sigil, but forgot to turn Protect From Magic on. I was teleprted to the arena and then the Jungle Demon killed me in 4 hits before I realized what had happened. Talk about a rough day for me!