With all the convex heads I've seen, the distance between the 2 blade edges does continue to get wider as you go further back on the blade - it's just that the angle of the sweep gets less and less steep.
Regardlesss of the shape of the blades, the whole blade should be as sharp as possible. Leaving the middle 1/3 dull will simply increase resistance to penetration and reduce the amount of cutting that the blade does accomplish.
With a concave blade, I would imagine (though have know proof) that the more tough, fibrous structures (eg. tendons, aponeuroses etc...) that MIGHT slide out of the way (along the edge of a convex blade), would more likely get cut by a concave blade. This may cause some reduction in penetration, but not enough to make any difference on almost all North American size game with legal bow weights & 2 blade COC boradheads.