The original manuscript reads “by night or by day”. Oliver Cowdery miscopied the or as nor in the printer’s manuscript. Either conjunction is possible here in this negative context (that is, within the scope of the preceding not). Elsewhere in the text, we have instances of either conjunction within the scope of a not:
There has been a tendency in the printed editions to consciously replace or with nor in such negative contexts. But some examples, as in Alma 55:19, have never been edited; for a list of other unedited examples, see under Alma 26:11. For a nearby example of the grammatical change from or to nor, see below under Alma 56:40. The critical text will restore the original or here in Alma 56:22.
Summary: Restore in Alma 56:22 the or of the original manuscript: “that they might not pass us by night or by day”.