Here the 1841 British edition replaced the singular record with the plural, despite the preceding two instances of the singular. The following LDS edition (1849) restored the correct singular. As explained under Omni 1:9, the original text allows for either number in the phrase “to keep the record(s)”, so in each case we follow the earliest textual sources, thus “which did keep the record” here in 3 Nephi 8:1.
Summary: Maintain the singular record throughout 3 Nephi 8:1.