Does a "Buck Step Down Voltage Regulator" provide constant output voltage regardless of input voltage?
A buck regulator that produces 13.8 volts may work down to an input voltage of 14 volts or 15 volts (circuit dependant). Once the input voltage gets too low, either the buck will shut-down or just turn on hard dropping a few hundred millivolts; if your voltage dropped to 10V then this type of circuit might be able to output 9.5V under load.

If you want a regulator that provides a constant output of 13.8 volts when the input range is from below 13.8 volts to above 13.8 volts then look for a boost-buck type circuit.