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fran·gi·ble
Pronunciation: 'fran-j&-b&l
Function: adjective
Etymology: Middle English, from Middle French & Medieval Latin; Middle French, from Medieval Latin frangibilis, from Latin frangere to break -- more at BREAK
: readily or easily broken
synonym see FRAGILE
- fran·gi·bil·i·ty

Is there any time when this word would be preferable or more appropriate over fragile?

It pops up now and then in art reviews, either as a more artsy way to describe ephemeral elements or (oh let's call them what they are) shoddy construction techniques on a piece too delicate to be moved much. It is also applied to the ego of a highly-strung artiste.

-gailr

Do you think that the lunatic fringe is frangible?

. . .
Is there any time when this word would be preferable or more appropriate over fragile?

From the American Heritage Dictionary entry from Fragile:

SYNONYMS: fragile, breakable, frangible, delicate, brittle These adjectives mean easily broken or damaged.

Fragile applies to objects that are not made of strong or sturdy material and that require great care when handled: fragile porcelain plates.

Breakable and frangible mean capable of being broken but do not necessarily imply inherent weakness: breakable toys; frangible artifacts.

Delicate refers to what is so soft, tender, or fine as to be susceptible to injury: delicate fruit.

Brittle refers to inelasticity that makes something especially likely to fracture or snap when it is subjected to pressure: brittle bones.

See also synonyms at weak.

Do you think that the lunatic fringe is frangible?

One could say that, by definition, they have already experienced a break.
-gailr