I've actually figured this out, but as I couldn't find an answer online, I'm posting anyway in case someone else has the same problem, which seems fairly likely as there's no warning or message from NetSuite about the issue and it doesn't cause an error as such.

I was trying to update a list/record type custom field we have that stores a reference to another transaction, e.g., "Invoice #<document number>", but although the import was saying it was completed, nothing was happening to the field and it remained empty.

It turned out that the mapping was matching the field name "FOC's Original Order" because it matched on the import file, but it was unable to process the input because of the apostrophe in the name. It was necessary to remove it from the file and manually map it instead.