The 1902 and 1905 LDS editions introduced the singular persecution, which the current LDS text continues. This change may be a typo since elsewhere the text retains the plural in nearly the same context:
More generally, the earliest text has 12 examples of the plural persecutions but only 4 of the singular persecution. Since either singular or plural is possible, we let the earliest textual sources determine the reading for each case.
Incidentally, the object pronoun them in the conjoined predicate “and destroy them not” apparently refers to destroying the prophets themselves rather than to destroying the words of the prophets. The following passage supports this interpretation:
Even so, there is one reading where the phraseology about destroying the prophets refers to that section of prophetic writings in the Hebrew Bible that is traditionally referred to as “the prophets”:
However, this interpretation for prophets does not apply in 2 Nephi 26:8; there the text explicitly refers to “the words of the prophets”.
Summary: Restore in 2 Nephi 26:8 the plural persecutions, the earliest reading for this passage.