RTC not running when power disconnect.

I'm using a DS1307 RTC module, It was working normally but now when i disconnect the external VCC, the module stop working and show me the "RTC not running" error.
this is my void setup() code:

if (! RTC.isrunning()) {
   Serial.println("RTC is NOT running!");
RTC.adjust(DateTime(2020, 6, 10, 11, 57, 0));

After one time that error happens and RTC.adjust() command works and sets the time, it starts working normal again, until next time I disconnect the VCC.
I thought it may be battery problem so i measured the battery voltage and it was 3.5v (which should be 3v depending what is written on the battery?) and also measured the voltage of battery pins on PCB to make sure battery is good in place. all were correct.
I don't know what else should i do, help me please.

Do you have a link to the specific DS1307 module you are using?