This likely means that your browser isn't allowing the game to save cookies or there is an issue with an adblocker.
If you come to the discord I (or someone else) can set you up with a downloadable version of the game that will save your file locally instead of into your browser data.
The discord is found on the main menu of the game. If you mean that the main menu won't even come up in your current browser, you should be able to temporarily open it in a different browser, and click the discord link there. (Don't bother playing it in a browser that's unfamiliar with you, you can close that browser once you click the discord link)