IPhone 4S dying even though it shows battery still has power 20-40%?

The phone is new I haven't had it for a month and its already giving me problems. It's dying before it hits 0%.It start dying at 0 but then slowly started dying with more battery left. What might be the problem? What could I do to fix it?

Mine has the same problem.
It will show about 20% left and then the next second die.
There's no real way to fix it other than keep an extra charger with you as often as possible.

Try deleting your recent apps that are still running by quickly double clicking the home button and all your running app appear and hold one until they all are shaking and click the (-) on all of your apps. Should keep it running until at least 4%

Most likely this is due to damage to your battery.
This most often occurs due to electrical surge, especially as many phones are left on chargers overnight which are not protected by surge suppressors.

Given that your phone is still new, I'd suggest starting with taking it into your local Apple store (or retailer from whom you purchased it) for a diagnostic on the battery. It can likely be repaired, but may require sending it off to do so.

Going forward, I always recommend an inexpensive battery backup for your bedside table.
I plug my phone and tablet charges, as well as my alarm clock into the battery side.
That way, even if there's a power outage in the middle of the night, I always wake up on time to fully charged devices.
You will want to setup the battery backup using a PC first to turn off it's annoying "lost power beeping" and to tell it to stay on as long as possible so that your devices get fully charged.
Even a $40-50 battery backup will charge your phone for days as well as giving you great protection against surge.

One final tip… Avoid using super cheap cell phone chargers found online. Many of these do not meet the manufacturer's specs and can't only damage your phone and battery, but also potentially yourself.

Apple has had such a big problem with this that they have started an official trade in program to get people back into safe Apple chargers for their phones.
http://www.apple.com/...-takeback/

Best Regards,
Covert Agent Andrew S.
Badge # 4418

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