It's not going to evolve, there are too many reasons against it.
Reasons that you probably have in mind:
1. Buizel is strong enough as it is and doesn't need to evolve.
My response: Chimchar was also very strong. No doubt stronger than Buizel. That didn't stop it from evolving. Turtwig was also very strong. There are many other situations as well.
2. Buizel has pride and it's pride will not allow it to evolve.
My response: Treecko, Tailow, Piloswine and Charmeleon all had that same pride but evolve anyway.
3. Buizel defeated it's evolved form
My response: There wasn't much, if any, tension between Buizel and Floatzel. Pikachu was determined to defeat Raichu, Croagunk hates Toxicroak, and Dawn's rival owns Piplup's evolved form. The only "tension" involving Buizel during Ash's battle with Wake was between Pikachu and Buizel.
4. Buizel was a promotional pokemon for the DP series so it's more popular
than it's evolved form.
My response: The starters are obviously more popular than their evolved forms and so many of them have evolved.
5. It's evolved form looks too similar
My reponse: Not really. It has like fin-blades on it's arm and it's floatation sack takes up most of it's upper body. It's face no longer has that round shape, now it has a dog-like nose.
6. Evolving wouldn't do much for it
My response: Well it would become bigger, faster and stronger. All evolution does that so really this excuse can't be used for pokemon in the anime. If you want new attacks then ice fang is a nice example. Not enough? Well I believe the writers don't allow certain pokemon to learn attacks because they would look awkward doing it in the anime due to their body type. For example, Buizel's arms are probably too short to make any sort of punching attack look natural in the anime. Floatzel's arms get much longer so punching attacks would now be avaliable.
7. It's too late and I think Buizel will be left with Oak at the end of the saga so what's the point of evolving it this late?
My response: Well, considering they've evolved one of Ash's pokemon at a pace of one every 15 or so episodes I don't think we're too pressed for time when it comes to evolution. At that pace they could easily squeeze in both Buizel and Monferno's evolutions before Sinnoh ends. If you're one of those who thinks Buizel is definately going to be left with Oak at the end of Sinnoh, so what? It's not like they haven't evolved pokemon late in the saga before. Glalie evolved late and then got Oaked. Donphan and Sceptile only battles in two major battles each after evolving. If Buizel evolved now, Floatzel would get the entire league to have a few battles. Surely that's enough if you look at Sceptile, Glalie, and Donphan's battle record after evolving.