Why does Safari no longer save flash game progress? I don't play flash games a lot. In fact, I try to avoid flash whenever possible; I just don't like the thing. However, there are a few games I like to play in my free time, like Amorphous+.

Lately (I can't tell you which OS it started happening on, but it happens on Sierra and it didn't happen, back when I was using Snow Leopard), whenever I restart my computer all progress made in those games disappears.

I understand these games save your progress by storing information somewhere on the computer's hard drive. If I right-click on the flash game, I get a contextual menu which includes the options "Settings" and "Global settings":


If I select "Settings" and then go to the "Local storage" tab, the option to allow the website that hosts the flash game to save files to my computer is selected. 
If I select "Global settings" and then go to the "Storage" tab, the selected option is the one that says "Allow sites to save information on this computer".
I just found a solution!

Go to Safari->Preferences->Privacy. For cookies and website data, check "Always allow". Refresh the page and the games save correctly. But you need to risk your privacy doing so.

Edit: It could be Kongregate changing locations of Flash game file recently causing this issue.

Edit 2: I think I found the cause of the issue. I have compared the source code of some webpages on Kongregate. On the pages where the games do not save correctly (such as Anti-Idle: The Game and Amorphous+), there is a string "konggames" in the source code. In the previous states as on Web Archive, there is no such string in the source code. To show that this is indeed the cause and not just the same string appearing everywhere on Kongregate, I checked the game Solarmax 2 and found that the game saves correctly and of now, and there is no string "konggames" in the source code.

This means that Kongregate has recently changed the host of some games to this "konggames" thing. By choosing "allow cookies from websites I visit"  or stronger settings in the preference, you effectively caused Safari and Flash unable to load save correctly because you have not visited the site "konggames".