Dando uma vista de olhos rápida no manual:
Backup Supply Input for Any Standard 3V Lithium Cell or Other Energy Source. Battery
voltage must be held between the minimum and maximum limits for proper operation.
Diodes in series between the battery and the VBAT pin may prevent proper operation. If a
backup supply is not required, VBAT must be grounded. The nominal power-fail trip point
(VPF) voltage at which access to the RTC and user RAM is denied is set by the internal
circuitry as 1.25 x VBAT nominal. A lithium battery with 48mAh or greater will back up the
DS1307 for more than 10 years in the absence of power at +25°C.
Mais à frente:
When VCC falls below 1.25 x VBAT, the device terminates an access in progress and resets the device address counter. Inputs to the device will not be recognized at this time to prevent erroneous data from being written to the device from an out-of-tolerance system. When VCC falls below VBAT, the device switches into a lowcurrent battery-backup mode. Upon power-up, the device switches from battery to VCC when VCC is greater than VBAT +0.2V and recognizes inputs when VCC is greater than 1.25 x VBAT
No resto do manual só fazem referência a Vbat a 3V, que faz algum sentido para o limite de funcionamento do mesmo. Suponho que se a pilha não estiver boa, apareçam umas tensões manhosas no pino de Vbat e isso confunda o chip... porque senão, não faz sentido o chip não funcionar quando se liga o VCC.
Importas-te de medir quanto tens no VCC?