Typically, for an engine equipped with an alternator to properly charge the battery, it would have to be run at full throttle for more than 15 minutes at a time. There are several reasons why the battery would not hold a charge. Some possible causes to this as well as other alternator related problems include:

BATTERY NOT CHARGING

Engine RPM too low Inline fuse "blown" (if equipped)

Defective battery

Loose, pinched, or corroded battery ground leads

Loose, pinched, or corroded battery charge leads

Open, shorted, or grounded wires between output connector and battery

Defective diode (open or shorted)

Defective or improperly grounded regulator-rectifier

Diode installed incorrectly (reversed)

Damaged battery (shorted battery cells)

Excessive current draw from accessories

Damaged alternator magnets

Defective stator

BATTERY IN STATE OF OVERCHARGE

Severe battery vibration (missing or broken tie-down straps)

Battery rate of charge not matched to alternator output

Defective regulator

HEADLAMPS NOT WORKING

Inline fuse "blown" (if equipped)

Defective headlamps

Loose or corroded wires

Open, shorted, or grounded wires between output connector and headlamps

Light switch defective

Damaged alternator magnets

Defective stator