The DS1307 is designed to be connected directly to the battery. R9 should be 0 Ohms. The current taken by the DS1307 should only be around 350 nA, and R9 will reduce the voltage by about 0.2 V but if the current taken by the DS1307 has any peaks, the voltage will drop further.
R10 will reduce the voltage to the DS1307 by taking extra current and giving a much larger voltage drop on R9 (unless it has been changed). R10 will also discharge the battery and take nearly 10 times as much current as the DS1307.
R5 and D3 provide a really crude and possibly dangerous recharging circuit for the battery. A CR2032 is not rechargeable so that circuit could cause damage to the battery.