I don't get what you mean, tried to reproduce your bug by saving, loading save, making multiple save didn't get anything weird. Note that the phone is now keeping on and on the last open app even after passage change except if you quit the app or turn it off yourself.
I'm on Windows 10 playing the game in an up-to-date Chrome.
Alright, I started the game again to reproduce the error, and this is what I ended up doing to reproduce it:
Opened the Save screen and Saved my game, Clicked on Gallery on the Phone, then the square button on the phone, then opened the Save screen to see my save deleted.
There were other ways I ended up getting my saves deleted by using the Phone, but I can't seem to reproduce them now that I need them to write down.
Edit:
Had Phone turned on, made an action that switched screens, Phone automatically turned off, Turned the phone On, did another action, Phone turned off, I turned the Phone on, and the Saves had gotten deleted.
There seems to be something between the Phone and Actions that make it delete saves for some reason.