I am having similar problems.
A few weeks ago, I earned the Stormpike Battle Charger/Frostwolf Snarler from Korrak’s Revenge, but my mount total in the “No Stable Big Enough” achievement progress remained at 301.
I logged on and out of every. Single. One. of my characters, and it still didn’t update. My count remained stubbornly at 301.
I went through a few ticket reopenings trying to get to the bottom of this, and was eventually told that they could not help me; my highest character should be Mahnta-Bleeding Hollow, a 54 Horde Paladin, but logging on to her didn’t work, and they couldn’t fix this for me manually, so I should submit a bug report and hope for the best.
I no idea why Mahnta is my character with the highest number; I assume my Horde Rogue LW with 2 prof mounts all 3 class mounts should have been, or even my Alliance Druid I’ve mained for 13 years. It happened quite suddenly several months ago that I had to log on to Mahnta to get the total to update, and I hadn’t used her since freaking Cataclysm nor have I earned any Pally class mounts! Yet another bug?
Fast forward to just now. Yesterday, I earned the Obsidian Worldbreaker. Did this perfect, cross-faction mount give me a new tally in my achievement progress? Absolutely not. Even after logging on to my Horde characters my number did not go up from 301 to 302, let alone the 303 I should have by now.
My only idea is that perhaps none of these counted because I earned them on an Alliance character. Who knows? Perhaps it is a problem with the Anniversary mounts. Perhaps my account/characters are broken in some way.
I’ve read that Blizz fixed a bug where people’s anniversary rewards were unusable. Perhaps they didn’t fix it all the way?
In any case, at this point I’m scared to earn any more mounts for fear they’ll get lost in the shuffle somehow.