Corrupted profile works only some times
I have a my Firefox profile and a copy of its folder. After a certain amount of time launching Firefox with this profile, the history and cookies are missing in the browser, as well as some other preferences and data. What I do is that I close Firefox, delete the profile folder, duplicate the copy to a new copy and rename the original copy to match the profile folder name. The next time I launch Firefox history and cookies are here again. Then after 3 or 4 launches, they've disappeared again, so here I go again with the copies.
I don't know what causes the profile folder not to work after a few launches. One time the history was there again even after rebooting the computer, most of the time it disappears after a few hours (after a few relaunches of Firefox).
The profile originally became corrupted when I performed a cold shutdown of my computer while Firefox was open. I remember that when I booted again, my profile was well; it was at the next Firefox launch that the data was missing. I opened the sqlite files with the sqlite3 command line and they looked clean. Next time I launched Firefox the data was available again. I made a copy of the folder in case of, and there I am with the merry-go-round of copies.
Perhaps another method of recovering parts of a profile, instead of copying are these steps: Back up and restore information in Firefox profiles
Other investigations that might be helpful is to determine if there are any settings or add ons that are removing history, or cookies.
This would be in the cookie/history settings of the browser. I do not know if the settings are entirely copied, ideally they are, but I have not tested your method before.
Is there a lock file in the profile folder or a pref.js file? Remore the lock file before copying the corrupt profile as well.