LM2586 - Inductor Heats Then Burns
I'd suggest your B340A diode is avalanching since you are far exceeding its reverse voltage rating.
The diode must standoff the voltage you generate, so you need a voltage rating above your capacitor voltage. I'd use something in the 75-100 volt range, and perhaps an ES07B would suffice.
I believe you are exceeding the peak inverse voltage (PRV) rating of D4, the 40 V Schottky diode. During your switching cycle when the SW pin on the 2586 goes to 0 V, D4 becomes reverse biased due to the level at the output at the top of C34. With the output set to 57 V, this exceeds the 40 V reverse rating of D4. This can only be observed and measured with an oscilloscope; you cannot see this with a multimeter.
Whether this is the cause or there's still something else, I suggest you use a 60 V diode in place of the 40 V for D4.
More detailed explanation:
When the switch is off, charge is pumped into C34 and is drained off by the load. With the diode shorted, C34 no longer holds that charge when the switch is on, but quickly decreases toward zero. The feedback senses the drop and the switching controller commands a longer on time to build up a higher current in the inductor. When this on time becomes long enough, the inductor will saturate. When saturated, it no longer functions as an inductor, and the current through L10 will be limited by only its winding resistance and applied voltage.
D4 should have a voltage rating 3 times the expected DC output just for a 50% safety margin. The reason is that when C4 has 57 volts on it the diode sees both the 57 volts and the zero volts when the internal MOSFET is ON again. Now it has 57 volts on it in reverse. Then another surge of forward current.
The inductor is overheating due to D4 shorting out, so the inductor and the MOSFET get the capacitor charge fed back to them.
Insert a fast diode with at least a 200 volt rating and this problem will go away.