When you dock the remote, look at the top right of the touch screen. Does the battery symbol animate? I find that as the best way to know if the remote is charging.

You are right that the light goes out after a few seconds; its normal.

Is your S70 using WiFi? If so, maybe it is set to always have WiFi turned on (and thus the remote always on as well) and that means that your remote is always on the network and that will definitely drain your battery fast.