The main reason that convex grinds are not popular is that they cannot easily be maintained by the use of v-type systems like the Sharpmaker or clamp and jig systems like the Edge Pro. They require freehand work on some kind of slack medium, or a lot of skill and a flat hone.
Note there is a huge difference in the performance of a knife with a dual convex taper, one with a full convex taper, one with sabre convex grind (with and without a secondary edge bevel), and simply a knife which just a convex edge bevel (with a flat, hollow or convex primary grind). All of these have convex bevels of a sort, but they are radically different knives and thus should not be quickly lumped into one group.
Specifically, the dual convex grind gives very high cutting performance over a wide range of tasks, the highest flexibility and impact resistance, and maintains its cutting ability with extended sharpening. A sabre-convex ground blade with a secondary edge bevel has a low cutting ability in comparison and the edge thickens rapidly with extended sharpening.
-Cliff