Why are Purple Heart chess pieces so rare?

That's a very interesting question.  I can recall only seeing it used in boards - and beautiful boards at that.  I'll be very curious to read what Those That Know Things have to say..

[edit] Well, that didn't take long.  There's a number of sets (and boards) at HoS - just search for "purpleheart".

I found 6 chess piece sets at HOS and all of them were gilded, which is a term applied to boxwood chess pieces that have been coloured to imitate other types of woods.

I wondered what that meant - thanks for the info!  Your question stands & I'll just shut up and learn something now.  

Purple Heart is beautiful. I’m not sure how to keep it from fading to a brownish hue over time though. 

It's not easy to work with, it's fickle and turns brown over prolonged exposure to UV light so you would have to keep it away from sunlight. So while it is beautiful there is not much reason to make it considering other available materials, although you could perhaps still find it out there.

People fear the color change but if you are comfortable with maintenance and keeping it out of direct sun it will stay purple for a very long time. It is, however quite hard to work with. 

Educate yourself a bit on the janka hardness scale and you'll begin to see where different woods fall and you'll understand how hard purpleheart (2520) is in comparison to something like walnut (1010)

I can attest to the fact that it's challenging to work and it undoubtedly has tearout issues when planing boards to flat. Since I don't turn, I can't speak to how it would handle in the lathe, but I would assume it's hard on the cutters and can also result in tearout in that setting. 

I, personally, rarely use it anymore due to environmental impact concerns that I become more aware of as the years go by. 

From the wood database:

"Workability: Working with purpleheart can present some unique challenges: if the wood is heated with dull tools, or if cutter speeds are too high, purpleheart will exude a gummy resin that can clog tools and complicate the machining process. Depending on the grain orientation, can be difficult to plane without tearout. Purpleheart also has a moderate dulling effect on cutters."

Thank you Bryan, this is the answer I was looking for.

It turns beautifully. I made a pawn for my son out of it. I would be more than comfortable turning pieces for a set, it doesn't burn with sharp tools but it holds a fine edge and polishes up beautifully. Carving is a different matter, I've never tried carving it but I don't imagine it to be easy. However if one were to do a Chavet style knight (largely bandsawed and then sanded with little carving required) then it would probably be a breeze. 

Im currently doing a Dubrovnik set in what I believe to be Jatoba, it's also quite purple and hard as nails. Here's a photo.