Will my Cookie Clicker save last beyond a reboot?

Solution 1:

If you're ever unsure, you can always export your game by going to the Menu and clicking "Export save". You will get a code which you can then use to import the same game.

Solution 2:

Haidro's answer is the safest, but to answer the question, Yes, your save will normally survive a reboot because it is saved to a cookie (no pun intended). The save will not survive if the cookie is disallowed, which might happen on computers set to not use cookies, or if you are using something like incognito mode.

Cookies also normally will disappear after a period of time without visiting the website, typically 1 or 3 months. However, given the rate of updates and resets, thats probably not an issue in this case.