In the 'Riming Poem' in the Exeter Book (Thorpe, p. 354, ll. 57-62) appear the following verses:
Searo hƿít solaþ
sumur hát cólað
The white by craft grows soiled
Summer heat gets cold
Earthly wealth fails
Hatred grows hot
Strength gets old
courage goes cold
As many Tolkien fans know, the first element of the name of the fallen wizard, Saruman the White, derives from the Old English noun 'searo', which means 'craft,' quite often in the bad senses of 'artifice, wile, deceit, stratagem, ambush, treachery, plot.' And Gandalf recounts a conversation with Saruman in which the latter scorns his color:
'For I am Saruman the Wise, Saruman Ring-maker, Saruman of Many Colours!"'I looked then and saw that his robes, which had seemed white, were not so, but were woven of all colours. and if he moved they shimmered and changed hue so that the eye was bewildered.'"I liked white better," I said.'"White!" he sneered. "It serves as a beginning. White cloth may be dyed. The white page can be overwritten; and the white light can be broken."'"In which case it is no longer white," said I.'
It is at this point of course that Gandalf reveals that Saruman the White has been corrupted, and that whatever skills he possesses have now proven 'crafts' in the wicked sense. When seen later, after his overthrow, he is of course now clothed 'in rags of grey or dirty white' (RK 6.vi.983; viii.1020).
Given all this, and Tolkien's undoubted knowledge of the Exeter Book, it may be that we find here at least a part of the reason (aside from the obvious) for why Saruman was white to begin with, and why he failed in the end. Though Tolkien is not much known for irony, this conversation between Gandalf and Saruman may be dripping with it.
 As Tom Shippey notes in The Road to Middle-Earth (revised and expanded 2003) p. 123, Tolkien often uses the Mercian dialect of Old English in generating words rather than the standard West Saxon, thus ‘saru’ instead of ‘searo.’