You say the battery is fully charged. But did you do a load test, or just put a charger on it til either the light went out, or the amp meter went down? A marginal battery can show "full charge" in a no load condition, but drop as soon as a load is put on it.

Tech's comment is well founded especially if you've let corrosion form on the terminal, and the insulation jacket isn't sealed at the end. The corrosion will migrate under the insulation, and cleaning the terminal end (as most people do) won't deal with the hidden corrosion.