No
There is no evidence to suggest that any one Nature is rarer or more common than another. With the exception of Everstone breeding or the Synchronize ability, Natures appear to be random.
Make sure you don't accidentally have a Hardy Synchronize Pokemon leading you party (pretty sure you don't, else the number would be closer to 12/25).
Also, ensure that whichever Pokemon is holding the Everstone has the ability you desire.
A final point is, competitively speaking, useless natures far outweigh useful ones, due to the limited roles Pokemon can play. Further, all neutral natures are essentially the same, meaning you have a greater chance of getting a neutral nature than a unique nature that has a unique effect on the stat.
According to Bulbapedia, though,
From Pokémon Black 2 and White 2 onward, a Pokémon holding an Everstone will always pass its Nature to its offspring.
so check into that, to make sure you have everything right.
