Question: did you extract the .zip file into a folder and run the game from the folder? Or did you just "open" the .zip file by clicking on it and run the game like that?
If it's the second, the reason the saves are disappearing is because when you open a .zip file with Windows Explorer it's actually extracting the .zip to a temporary folder behind the scenes. Windows doesn't keep track of changes to the temporary folder (like save files), so they're lost when you close it.
You need to right click the .zip file and select "Extract All" to turn it into a normal folder. That way Windows won't keep creating new temporary folders and losing track of your saves.