By using electrolysis one can separate hydrogen and oxygen, but when burning hydrogen and oxygen together steam is released, therefore creating water. My question is:
how much of the original quantity of water would be lost after this process?
Actually, since the gases are produced in a damp environment, there would be a lot of water vapor in the gases. You could easily remove most of the water vapor, but some (maybe as much as 1%) would still be in the gases.
I think it would be best to elaborate on what you mean as water being lost?
In the example of a system electrochemically (solar panel) splitting water into hydrogen and oxygen storing them, then burning the gasses, in an ideal system there would be no loss.
However, hydrogen is a very small molecule that can intercalate into materials, there by slowly diffusing outside of the system (and potentially embrittling them see: https://en.wikipedia.org/wiki/Hydrogen_embrittlement). Furthermore, any small defect in a seal on the hydrogen storage and delivery side of the system would cause a substantial loss of hydrogen.