A few things can help:
As you're working it, try to keep it clamped or sandwiched between two two flat surfaces as much as possible, especially when you're not working on it. Even if this means pressing the blade down onto a table using some books, keeping it pressed against something flat will keep it flat. Moisture in the paint, air, sealant, etc may seep in and warp the wood as it dries/cures/hardens.
If you can brace it with something that won't warp, all the better. If you can embed a metal rod inside, that should keep it from warping. Plastic might even work as well if the wood is thin enough.
Always store it with the blade supported in a way that relieves pressure from just one spot. Don't store it on its tip, on the pommel (end of the handle) or leaning against something, as gravity and its position might put stress on the blade. Lay it flat, with the full length of the sword being supported.