I'm trying to get my Eevee to evolve into a Sylveon, but its Pokemon-Amie stats keep decreasing. Is there a certain place I need to be, or am I doing something wrong?
For Sylveon to evolve, you need to max out the Affection stat. (The love hearts) Eevee may be as hungry or bored as you plan for it to be, but it needs to have a maxed out Affection stat in order to evolve.
And with that, the Affection stat doesn't decrease. So just keep on petting it sooner or later you'll have a Sylveon. As for the other stats, you need to play with it and feed it PokePuffs a lot more than what you're doing now. x)
Read this article on how to increase affection. (I haven't read it, but it can't be that bad, can't it? xD)
Hope I helped. :)