If you remove the first loop() then loop is only called when serial data is entered.
Try something more like
bool sleepMode = false;
void loop() {
if (!sleepMode)
DW1000Ranging.loop();
if (Serial.available()) {
int state = Serial.parseInt();
if (state == 1) {
sleepMode = false;
DW1000.spiWakeup();
// don't know if some other re-initialisation will also be required here or not.
// maybe try a short wait and then soft reset if it doesn't work as is.
Serial.println("ON");
}
if (state == 2) {
sleepMode = true;
DW1000.deepSleep();
Serial.println("OFF");
}
}
}