The bug: There is no sound, animation, or indication in the pet battle log that your leveling pet gained any experience or leveled.
Following the exact team and strategy for Aki the Chosen in Vale of Eternal Blossoms from the famous 5.4 Tamer guide: http://www.warcraftpets.com/community/forum/viewtopic.php?f=10&t=7556
I'm not sure when this bug began happening or if it's always been like that, but here are two screenshots showing it:
1. My level 14 Lil Smoky being swapped in between turrets: http://i.imgur.com/Ef7hHpr.jpg
2. Level 20 Lil Smoky with no indication anywhere how much exp he received and what level he jumped to: http://i.imgur.com/wOPOr6a.jpg
I'm too lazy to submit a bug report. Feel free, anybody.™