The clock time is keep by a battery or capacitor on some models (not the main one) but a small one on the motherboard when the computer is off.
When the computer is on and online it will automatically update the clock time.

Normally that battery last 3-5 years. 

Try setting the time manually, by getting the actual update for apple time server.

> sudo ntpdate -u time.apple.com

then you will see something like

> 8 Jun 14:30:11 ntpdate[28267]: adjust time server 17.151.16.14 offset
> 0.000336 sec

You generally don’t need to do this if you use the “Set date and time automatically” feature within the Date & Time settings.

![enter image description here][1]

If that did not work, reset your SMC and PRAM ([System management Controller][2])

I can not believe it is your battery but everything is possible :(. Assuming you do not have 2 left hands, you could do that your self.


  [1]: https://i.sstatic.net/HYjjn.png
  [2]: http://support.apple.com/kb/ht3964