Roger,
I looked up the current draw of your 385ci and it is only 300 mA. ( or 1/3 of an Amp)
If I were you I would upgrade my 12V battery to a 9 Amp hour version. The standard battery that comes with most portables is 7 Amp hour.
A standard 7 Ahr battery should easily run for a full day without issues.
Maybe you could turn down your brightness on your unit to help increase your run time. Also make sure all your connections are clean and tight. Use a good quality charger made for your battery and make sure you are 100 % charged each time you go out.
In Kingston, I buy my batteries at National Battery. They have 9Ahr batteries at good prices, along with small battery chargers.
Good Luck,
BATMAN