iirc tomodaci life saves to the consoles SD card, not the cart, so its probably the SPI save chip dead in the cart
im not too sure how the sky3ds handles CARD2 games, but i know with the gateway 3DS if the SPI chip died, only card2 games would work (pokemon X/Y/OR/AS/S/M, animal crossing and a few others) as the cart used a different method for saving with those games