From a review of Enya's "Amarantine" CD -

Named after a mythical flower that never fades, the theme of Amarantine centres around enduring spiritual love – how we yearn for it and strive towards it.
http://enya.sk/articles/amarantine-review4.htm

Ok, im panamenian and this flower as know as COLA DE GATO english traslate is CAT TAIL, interesting because i always thougth that amarantine was a little pale-purple flower ...cool see ya

hi! Amarantine comes from the greek word αμάραντ ος or amarantos written in english characters which is formed by two words(α)a=un + the verb (μαραίν ω)maraino= to wither/to fade out.

The meaning of the word is 'the one that does not wither/fade out/die'
According to the greek mythology, amarantos was a flower hidden by gods. The person who will find it, will become immortal. A whole family of herbs was named after this mythical plant. I think i sufficiently answered your question. Byee :)))

"Amarantine can refer to:

Amarantine (album), a music album by Enya
Amarantine (song), a song by Enya
The word amarantine, or, more commonly, amaranthine, has several, generally related, meanings:

of, related to, or resembling, the amaranth genus of plants (including the flowers and grains called amaranth)
of, or related to, an imaginary flower that never fades
unfading, everlasting or immortal
of the colour amaranth - a shade of deep purple-red
It is commonly used in the forms amaranth or amaranthus, in reference to flowers of specific orders. There is no such word as 'amarantine' in standard English dictionaries, but 'amaranthine' is referred to in Amercian Heritage Dictionary (Houghton Mifflin Co, 2000). However, Enya has derived it from the Greek "amarantos". It has been used in a variety of forms by artists in the past under poetic license (including amarantine and amaranthine)."
Source and further information:
http://en.wikipedia.org/wiki/Amarantine

Enya---Amarantine
http://www.youtube.com/watch

It's not in the English dictionary, but it can mean unfading.