how do you load your saved game?
Viewing post in Taiyaki Fabulous Museum of Fish comments
Normally, if you saved by talking to the floppy disk at the Looong Gallery, the title screen has a 'continue' option.
I'm not sure if you're playing in the browser or with a downloaded copy. If the browser didn't save your game, you might have some browser setting that is clearing your cookies.
I really recommend downloading the game and playing on your own emulator. I'm sorry to hear if you lost some saved progress.