Baking soda is merely bicarbonate of soda and shouldn't be adversly affect by age. Baking powder, on the other hand, will definitely be affected by age and lose some of its leavening potential.
That being said, I would have to think that mixing more air into the batter, either through vigorous whisking, or the use of an electric mixer wouldn't help the volume.
Your carrot cake rises due to the carbon dioxide given off by the chemical reactions of the acid and alkalye ingredients in the baking powder, and by the alkaye baking soda reacting with the acidic egg-white. Also, the egg protien couple with the wheat gluten helps trap that gas, causing the cake to rise.
Are you using a double-acting baking powder? This has more leavening power than ordinary baking powder. Also, the amount of oil in the recipe can make the cake heavy. Cooking too quickly can have an adverse effect. When you make the original recipe, do you cook both cakes simultaneously? That will cause the available heat energy to be devided by the two cakes, increasing the cooking time. This may allow the cakes to rise better. If that's the case, decrease the oven temp by about fifteen degrees.
I have found that adding additional baking powder, about an extra tsp., will make the cake lighter, but can also make it too "loose". That is, the crumb won't hold together. The cake will literally crumble when trying to remove pieces from it. But your cake is too dense, and this might just do the trick for you.
My recomendation, decrease the cooking temp, and add an extra tsp. of double-acting baking powder to the recipe.
Seeeeeya; Goodweed of the North
