It is because even the online version of HTML games are using local data storage, the cache or cookie storage area of the browser. If you delete the cache, or you played in incognito mode (which clears such data after closing the browser), your save is lost. In this case (or if you wish to play on multiple devices), you should save the game on local disk separately. However, as I see this game doesn't have that save/load option, therefore the only choice to keep your save is to play the game in normal mode instead of incognito, and don't delete browser cache and/or cookies. I think it is true for the offline version too, because the browser itself handles the saving of data in its own storage area instead of the game's local folder (but not sure, I'm playing on the online version).
BTW exporting/importing the save would be a useful function, as the game has a very long story, even 1 ending can't be finished in a day if you are playing it first time. It would be shame if we would be forced to skip the text because of this. So far I've completed 1/30 ending only (the Daemon ending, and its counterpart of that path which wasn't finished) in 2 days, and the story was awesome. It worths to read everything, it is exciting, arousing, surprising, makes the player to think. I still don't know answers to many questions.