My Braixen's been doing this a fair amount as well. So far, the only change I've noticed is that it gains a little bit extra experience at the end of battles. We'll probably learn more about Pokemon-Amie and how it influences stuff later on. If it's replaced happiness...well, that certainly explains my Azurill.
"Now when I tell you to ascend to a higher plane of consciousness, you say HOW HIGH SIR?" --Bucky Katt