[MargeSimpson]

I love this plant and I'm on my third one. The first two went the same way my third one is going. I thought I had learned from previous experience but alas, no such luck.

The stems and leaves dry up and die. I'm left with one good leaf surrounded by tall dead ones. I can't find any evidence of bugs, mites, etc.

This time, I only watered with rain water, I put the plant standing in a tray of stones, so as a) not to have the plant standing in water and b) to create a more humid environment.

Anything else it could be?

[birdie]

Sunlight magnified through a window possibly. They like it bright but not scorching bright. They like to be misted also and fed about once a month. you are avoiding waterlogging so that is good and you say no bugs but one possiblity is spider mite as they are tiny. any sign of fine webs on the plant from the mites.

[Liparis]

I agree with everything there.
They prefer bright shade to bright sunlight, even plants which like bright sunlight still need it filtered when coming through glass. Try it on an east or west window, but back from the window a bit. The name Parlour Palm says it all. They were very, very fashionable in Victorian times, nice and handy for growing in dingy, cool parlours. Cool is the other operative word. It sounds like it's suffering from bright, dry conditions, but it could be taking up water by cappilarly action from the gravel. Try and put something in the gravel to raise the pot off it, it just needs enough to break the cappilary action. Three insects just love Parlour palms, Red Spider Mite as Birdie says, you can see them with the naked eye if your young enough, a small magnifying glass if your eyes are poorer. The other bugs are mealybug and Scale.
Spraying with water several times a day helps control red spider mite, Isopropyl Alcohol kills scale and mealybug.
Bill.