Oops, not sure if you're still having this problem, but it seems I may have misunderstood, so I'll chime in again- if only to link in case someone else shares this problem. pretty sure a necro here is 2 weeks so I'm good
There are 2 methods to saving:
Save, which deposits the save in a folder located in various areas depending on your chosen browser and play method. Listing
all of them is both exhaustive and a hassle, so check the quote below for methods of finding the location. You need to create a proper Save to search for first though.
Save Locations:
-Windows: Hit Windows key + R > Type %appdata% and hit OK > go to the search bar and type .sol > wait 30s and all your TiTS/CoC .sol saves should pop up
-Mac: Either search .sol, or go to ~/Library/Preferences/Macromedia/Flash Player/#SharedObjects/ If not there, it'll be a little further in #SharedObjects/<random numbers and letters>/localhost
And
Save As, which allows you to choose a save location of your preference.
Since you lost your saves your goal in this is to create a back up. It appears the second method may only work when playing the offline version, in which case Hatter's directions will work. However, if you'd rather continue playing off this site, use the method in the quote to find the folder, and shortcut it. Copy the .sol(s) into a back up folder located wherever you like. Should you lose your saves again, you can copy the saves from the back up folder back into the shortcutted location. The caveat of this method is that periodically copying saves to your back up folder can also be a hassle.
I know suddenly losing all your saves can be frustrating, so I hope you figured something out.