Can I split water without constant refill of solution?
Salt is not needed. Salt merely allows the water to be somewhat more conductive. 

The King of Random on YouTube has a great video on making one. All you need is electricity and water. 
https://www.youtube.com/watch?v=cqjn3mup1So

He uses sodium hydroxide, but this not needed. It will just be less efficient. 

If you want to be more efficient, you can add an electrolyte like salt. Whatever electrolyte you use, should not be used up. However, if the concentration of electrolyte gets to high (after you have used up a lot of water) it will split it too. This is bad with salt, as you can end up with chlorine gas and sodium hydroxide, which can be nasty to deal with.

So, as long as you replace the water fast enough and don't put in too much electrolyte, it should be fine and you will not need to replace it often.