There’s nothing posted in the instructions included with the Logitech Dual Rumble Cordless Gamepad about this, so I felt it would be a good idea to share this information.
If your controller suddenly stops working, or if the red light on it starts blinking, and it will not connect, attempt to reset it. This is done by taking out ONE of the batteries, holding down buttons 5 and 7 (these are the two right-hand huddle buttons) and re-inserting the battery.
Hopes this helps some people out.