Electronic Problem about Freewheeling Diode?

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It sounds like this may be a brushed motor and the brushes are burned or the springs are shot.

It sounds like the inductive kick is exceeding the specs of the diode. Replace the brushes and the diode.

The Diode is good for this application. You can parallel two diodes to handle the spikes but replacing the brushes should be a good fix.

When you turn power off, you will have a current of 46A flowing through the diode for a short time (current ramps down to zero over some time period). If you look at the spec sheet, this diode will dissipate 46 W at that current level.

The thermal resistance is around 50°C/W which means your diode will get up to 2300 °C if the current is continuous. Since we don't know the spin-down time of your motor, hard to say, but if you put your finger on the diode and it burns you, the diode is underrated.

What you need is a diode with higher current capacity (in the 15 to 50A range) that can be attached to a heat sink. Probably in something like a TO220 case, or larger.

Because its peak voltage is too low, just 40V that ever able to stand the counter EMF is generating from motor while switching on and off. From my past trouble shooting experience on Schottky Barrier rectifier commonly burnt open easily. Replace it with higher voltage type can be avoid this trouble,or parallel a 36v transorb diode to it.

A lot depends on how frequently you turn the motor on/off. The diode prevents arcing in the motor switch when the motor is turned off, thus it only sees current at that time. 

But that current persists for a while, how long depends on the motor inductance and resistance. but not instantaneous.

550 w and 12 v is 46 amps. For safety, you would want a 50 amp diode, but those require a large heat sink. The ones I know of require a press fit hole in a large hunk of aluminum.

A compromise may be a 1N3208 which is a type that bolts to a heat sink. It is rated at 15 amps DC and 250 amps repetitive surge.

Assuming this is an external freewheel diode to prevent arcing when turned off, it comes down to asking if the current is "instantaneous". In data sheet this translates to mean momentary ie just for an instant. 

Your motor has a DC current of 550W/12V = 45A and when switched off, that current will circulate round the coil and diode until the stored energy dissipates as heat. I don't know what the time constant is of the coil and its resistance but with 45A going through it nothing is going to be instantaneous. 

If I was selecting a diode for that role I would want its nominal DC rating to be 50A continuous (as distinct from 3A for a 1N5822). The fact that the 1N5822 works at all suggests that a 50A diode is probably overkill, however, even tho it may be overkill and  cost you a few $ for one diode, it will never let you down.

The 80A figure in the datasheet is for "Non-Repetitive Peak Surge Current". You are repeating the surge every cycle. The diode itself is only rated at 3A continuous.

You need a diode with a much higher current capacity. Say 20A.