Well, it could be the charge. To make sure that isn't it, be sure you leave it on a charger for multiple hours. They need that if they get completely drained.
Also, it could have been a bad battery. Lastly, it could just be a faulty tablet. The problem becomes that you waited this long, it may not be under warranty anymore. I would check with the place where you bought it, and if not them, the manufacturer.
Unless you damage a device (drop, spill something on, sit on, etc.) it should work and work for quite a while when you have just bought it.
Check into warranty/returns first before trying anything that could void the warranty.