My understanding is that the Rainer/Sparky/Pyro trick (name your Eevee one of those names to select the corresponding evolutionary track: Vaporean/Joltean/Flareon) works only once for each name.
This seems a reasonable move on Niantic's part, giving players the ability to secure at least one of each type, while having it be a random outcome most of the time, just like hatching an egg - having it permanent would effectively mean every evolved Eevee becoming a Vaporean (that seems to the overwhelmingly popular choice).
The Eevee name trick has been called the game's first Easter Egg. The Niantic folk have said as much, and have said there are others no one has found yet, but I don't think they've detailed the precise rules for this Easter Egg's mechanism. Some folks have reported it working multiple times, but remember, you have a one-in-three chance of getting what you wanted anyway - this likely explains occasional reports of repeated success.
The downside is, not knowing this, or missing other bits in the game's learning curve (it outwardly seems simple but there's all sorts of interesting math folks are trying, to get the best possible Pokémons), might mean evolving less powerful/optimal Eevees with one or more of the "single use only" names, and then being sad to find it's not repeatable.