It could be these things:
1) It's a glitch
2) Your Poffins somehow didn't max out your Feebas's beauty.
3) You transferred it from a 3rd/4th gen game,e.g. sapphire or diamond to a 5th gen, like white or black 2. Reference to the #.
4) Some other obscure thing(s)
I recommend you breed your Feebas or catch another one and try again. Same thing happened to me, I bred my Feebas and that one evolved.
(#) The difference is in gen 5, you need to have a prism scale and at least 2 DS/DS lite/DSI/DSI XL/3DS/3DS XL systems. You need to have a Feebas hol one and trade it in order to evolve. While gens 3&4 has that Beauty/Cool/Tough/Sweet/Smart system in the Contests.