Hair is actually keratin, a truly durable substance. Victorian hair jewelry has retained its original color and shape well under truly undesirable storage conditions. Bugs do not eat it.
One concern is brittleness, as the last traces of oils dry up. Once a piece of hair is mounted, so that it won't be flexing, that concern is dealt with.
Brittle hair will not break in response to vibrations or shocks, so there is no need to coat it with stabilizers.
The only other thing to worry about is color change. UV light will turn hair more blonde. Hairspray remnants will turn brown, or even black over the years. Dried hair will be less lustrous, and seem paler. (heat is the usual culprit) Dyed hair will react strongly with other chemicals around it, particularly acids, and there is no predicting how it will change. Bleached hair can absorb colors from oils or varnishes that touch it.
(naturally pale hair won't) Pubic hair is so oily it will stain matboard. (don't ask)