If the participle clause relates to the last item in the main clause, no comma is required. In the following sentence, for example, the participle clause applies to "dog".
He watched the dog wagging its tail
If the participle clause refers to something earlier in the sentence, a comma is required. In this sentence, for example, the participle clause relates to "the student".
The student was unable to understand the author's main point, finding the whole article virtually unintelligible.
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In your sentence, despite is a preposition, so it's actually a prepositional phrase. Check out rule 8, which states that a comma is required if a phrase of any kind refers back to the beginning or middle of the sentence. Your example is therefore correctly punctuated, because the prepositional phrase refers back to the student.
The student was unable to express the author's main point, despite having read the article several times.