The printer’s manuscript here reads many day, which the 1830 typesetter emended to many days. The original manuscript probably had days, and the s was therefore dropped while copying from 𝓞 into 𝓟. Another possibility is that the original manuscript had the colloquial phrase “many a day” and the a was accidentally deleted during copying. Both kinds of copying errors are possible, although Oliver Cowdery dropped the plural s considerably more frequently than he omitted the a.
There is no independent textual evidence in the Book of Mormon for the colloquial reading “many a day”. All except two of the 39 occurrences in the current text of “many days” read that way in the earliest textual sources. Besides the case here in Mosiah 18:7, there is one other instance of many day in the earliest source:
In this other passage, the 1830 compositor interpreted many day as an adjectival modifier of repentance (he set the text as “many-day repentance”). Of course, Samuel the Lamanite was preaching long-term repentance (in contrast to short-term repentance), but this interpretation is clearly not what is meant in Helaman 13:2. Rather, the text intends to say that Samuel “did preach repentance many days unto the people”, but the original word order in Helaman 13:2 makes this sentence difficult to read. From the 1837 edition on, the text has read properly in the Helaman passage, thanks to some judicious punctuation (namely, the placement of commas before and after many days). For further discussion, see under Helaman 13:2.
Since 37 out of 39 occurrences of “many days” read as such in the manuscripts, but none actually read “many a day”, we should accept the reading “many days” for the two places in the text where the earliest extant text (the printer’s manuscript) reads many day. In both cases, a plural s was probably lost during the early transmission of the text.
Summary: Retain the reading “many days” found in the current text for Mosiah 18:7 (as well as for Helaman 13:2).