You may find that you get problems as you have used a breadboard. The breakout board in the article I pointed would have saved you much head scratching.
Try this ,
upload the sketch you posted. Watch the time tick away nicely.
Now disconnect the line from the battery to the chip all should still be well. With that line still disconnected, unplug the Uno from the PC and wait a few mins.
Now reconnect the Uno to the PC and open the serial monitor, the time reported by the RTC will be behind by however long you left the Uno disconnected from the PC.
This is because the RTC was rest to the time the sketch was built and uploaded.
However if you leave the line from the battery to the RTC connected when you disconnect and then reconnect the PC you should have the correct time.
BUT, if, while the Uno is disconnected from the, there is any glitch in the power to the RTC it will go back to the time the sketch was loader. And breadboards are a real pain foe giving glitches when moved.
Mark