1. Stop using IHasModel.
2. What is this NBT even for? You are not doing anything with it.
3. You never serialized the ItemStackHandler to NBT in your BeyBladeProvider, thus the content is not saved. You have the serializeNBT method, but it does not save the NBT of the ItemStackHandler.
(Hint: Creating a new and completely irrelevant NBTTagCompound and returning it in the serializeNBT method isn't going save your ItemStackHandler.)