Why does my cellphone keep turning off by itself?

I just bought my Xperia X10 , refurbished, on the 25 of May and it's already malfunctioning. I found out that something was wrong with my phone when I used Google's GPS for directions home and the phone turned off by itself. I had to turn back on three times before stopping altogether. Apparently it shuts down by itself every single time the smartphone is made to do a task that may be taxing on the battery, like using the GPS, browsing the internet, and even charging the battery! What's going on?