L6202 H-bridge keeps breaking when switching directions
During operation the DC motor will be powered with 48V


The data sheet first line says: -

SUPPLY VOLTAGE UP TO 48V 


Additionally, figure 47 (Bidirectional DC Motor Control) says Vs = 36 volts max.

The absolute maximum rating is 52 volts and it is likely that back emfs are pushing up the 48 volts supply beyond the absolute maximum limit. You are running too close to the absolute limit this device is intended form. Choose something that is 60 volt+ rated or implement a better supply that has energy dissipation facilities when the motor is being reversed.