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.