I think what you are seeing is not laser diode failure. It is most likely the natural variations of the wood itself, plus a slower feed rate causing some over-burning, and perhaps an excessively enlarged image(?).
The image itself is near all mid-gray shades, with un-sharp details, so there is not much spread in gray shade values that would normally help mask the naturally variable burn characteristics of the wood grain. Am I correct that the original image much smaller, and then enlarged quite a bit for engraving?
Can you post a picture of the complete engraving? It will help to see if I am correct about the wood grain causing your "zebra" issue.
You might try sharpening the image some before generating the gcode, and also use a larger pixel resolution (0.005" is usually too low for a laser diode), and use a higher feed rate. I am doubtful, however, that this image is going to give you satisfactory results.
Hope this is helpful.