Ipad 2 keeps powering off

I have an iPad 2 which worked absolutely fine until Christmas when i downloaded the ISO8 software. Since then it keeps powering off at random - when i am touching the screen or even reading a book - but seems to be when it is about 70% charged. The screen suddenly goes black and even when holding down the sleep/wake button to get the apple logo on the screen, the logo may only stay on a minute or so before the iPad powers off again. The only way i can power it back up to is to recharge to 100% at the mains. I have taken it to the apple store twice - and they say the battery is fine it is more likely to be a software glitch. On their advice i have reset to factory settings. Initially, this seemed to work for a week or so but now the problem has restarted. It is very intermittent but so frustrating since i can go for a few days with no problems and then it will start to play up. Apple have stated that if the reset didn't work, it is likely to be a hardware problem and i would be best buying a new device. I wish i hadn't downloaded the update since this seems to have been the cause of the problem. Any advice from fellow iPad owners would be much appreciated!