That's not quite right. In all the modern Tamagotchis (those made since 2004) there is a small amount of nonvolatile RAM inside. Your data (character type, age & other stats, inventory - gotchi points, food, etc.) are backed up there every so often. Generally, when your battery gets low, you can replace it with a fresh one, then press the reset button, and select Download from the Download/Reset menu to restore this data. Then you will see your character is back. (She may have lost a few hours growth time, but otherwise she'll be the same.)
When I'm not running a particular Tamagotchi, I remove the battery. For some, I've installed a fresh battery months later, and after selecting Download, I've been able to resume caring for the same character I left off with.