I can't reproduce this issue, could you please send a screenshot of the browser console when the tab becomes empty?
"loses quite a lot of time." what do you mean by that?
I've found an issue with worker allocation in Firefox and deployed a fix.
On the other topic, saved games should be the same on game.delvers.io and on znik.itch.io, and this is the case for Chrome. Firefox probably applies some third-party cookie protection, which affects local storage, too, so the games are different. You can easily download a game in one place and upload to another, if needed.