Thank you! First of all, I recommend checking the Choice of Games forums. They have many free demos, some of which are quite lengthy as well. I couldn't replicate the save-resetting bug on my end but found a guide here to export saves from the browser:
Open the developer console in the browser (Shift+Ctrl+I) and then to Local Storage on the Application tab. You'll likely see a mess of files left by choicescript games and others. The save files from choicescript plugin come in pairs: a file named game_name_savemod_name_X (the name of save in the save drop-down menu in the game) and game_name_savemod_data_X (actual game state data) Note, game_name_ is a string defined by particular game, e.g. "auraclash_" or "college_tennis_")
Since both of these files contain text data, you can copy/paste/save their content to files on your hard drive, and then restore them in similar manner, if needed.