tiny RTC DS1307 module not working with arduino

I am currently trying to interface an RTC with arduino. For this purpose,I am using Tiny RTC module purchased from Ebay
My connections are as follows-
Vcc-Vcc
GND-GND
SCL-A5
SDA-A4

I have downloaded the RTC library from adafruit website and am trying the example code.

#include <Wire.h>
#include "RTClib.h"
RTC_DS1307 RTC;

void setup () {
    Serial.begin(9600);
    Wire.begin();
    RTC.begin();
  if (! RTC.isrunning()) {
    Serial.println("RTC is NOT running!");
    // following line sets the RTC to the date & time this sketch was compiled
    RTC.adjust(DateTime(__DATE__, __TIME__));
  }
}
void loop () {
    DateTime now = RTC.now(); 
    Serial.print(now.year(), DEC);
    Serial.print('/');
    Serial.print(now.month(), DEC);
    Serial.print('/');
    Serial.print(now.day(), DEC);
    Serial.print(' ');
    Serial.print(now.hour(), DEC);
    Serial.print(':');
    Serial.print(now.minute(), DEC);
    Serial.print(':');
    Serial.print(now.second(), DEC);
    Serial.println(); 
    delay(1000);
}

Below is the Screenshot of the output I am getting using Serial monitor. I want to ask why does the output(date and time) come correct for the first time and after that becomes incorrect? I am really confused.