The second 'can' in your example is correct, but it isn't necessary. When you think about parallelism, think about the 'root phrase' - the part of the sentence that all of the parallel elements 'grow from'. Both of these sentences are correct, but they just have different root phrases, which I've bolded:
Danny can eat 20 donuts in a sitting and can run 15 miles without breaking a sweat.
Danny can eat 20 donuts in a sitting and run 15 miles without breaking a sweat.
As long as the 'parallel elements' all match each other, and they all 'fit' the root phrase, it's fine, regardless of exactly what the root phrase is.