In all the games I own, Eevee is the hardest Pokemon to catch. I can never find it even if I serch for over a hour.
Here are the possible locations for Eevee:
It would be fairly easy to get it in the HG/SS and FR/LG games because it is a gift given to you.
In Platinum/Diamond/Pearl, it is somewhat harder as it is considered rare.
In Black 2/White 2 , the chances of catching an Eevee (in the patch of grass in Castelia City) are similar to the chance of getting the Eevee in Trophy Garden (Platinum/Diamond/Pearl).
In X/Y, the yellow patch has the greatest possiblity of getting an Eevee (it's uncommon, which is better than rare).
In OR/AS, you have to use DexNav for an Eevee to appear (it's still uncommon).
I'm not sure what games you have, but the reason why Eevee might not be appearing is that the chances are somewhat low. That and it could be bad luck.
Hope I helped!
Sources: Above links