Personally? I think Edge just doesn't want to play 2nd fiddle to Triple H (can't blame the guy).
Before HHH arrived, Edge was the top heel and had Vickie backing him up (in more ways than one?

).
With HHH here however (and instantly being the world champ), I just don't think Edge wanted to be the guy to 'make Triple H look good' by jobbing. From what I understand, its been well documented that Edge has a major problem with Triple H's backstage pull...and has been outspoken about this.
Personally? I think the WWE might have Edge come back with a returning Christian.