Check the charging system. Start by measuring the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If it is low, stop the engine and do a continuity test between the two smaller wires on the back of the alternator. If it reads "open", irritate the belt a little to wiggle the pulley, then read it again. These tests have to be done when the problem is occurring. If you find an open circuit, the brushes are worn. They can be replaced separately but most people just replace the entire alternator.