Hi and Welcome to the forum,
Perhaps your power cord is broken in some way.
Try an alternative one to factor it out.
is your iPhone fully charged when you turn it back on.
If your jail broken look at the most recent tweaks you have downloaded and remove them.
Is your iPhone up to date with the most recent iOS.
Reset it by either turning it off and back on are by pressing the top button and home button until the apple logo appears and then let go.
If your not JB then hook it up to iTunes and perform a restore as a new device.
If all else fails then make an appointment at your Apple Store Genius bar.
Remember to remove any jail break if you have one !
