I can think of a few reasons for this:

An edge requires a certain stat to take. You put on some - stat gear, and you don't qualify anymore.

Anything that lowers your skill in something below the percentage required for that edge, ie berserk.

I will point out that if you take an edge and use up your edge points on it, you'll only be able to then see what edges are available to you with the current amount of points you have.

There will be no white flag above my door. - Dido

Stones taught me to fly
Love taught me to cry
So come on courage
Teach me to be shy
Cause it's not hard to fall - Damien Rice

What doesn't kill you makes a fighter, footsteps even lighter - Kelly Clarkso