Why does my cell phone keep turning off when I get it off charger?

[ShaquishaF]

I charge my cell phone up,and when I take it off charger the phone shut off...completely! I have and Motorola Droid,verizon is the plan! If you know how to fix it or what's wrong,please help! I will try anything! Please don't say buy another phone,I just bought this one! I don't have insurance,I know that's was a bad idea! I would take and advice or suggestion to what wrong..thank you!