What's the exact version of Laserfiche being used? What version of Laserfiche was used when these documents were initially imported and had metadata set?

One explanation is that in the database table that contains the field values, some documents that don't have a value for AxysNum do not have an actual row in the propval table for that specific field with a NULL value. Therefore, those documents aren't coming up when you search with [AxysNum]=""

Since there seems to be seven documents that fall into this particular category, what I would do is find out the specific documents that are assigned that template and missing a row in the propval table for that specific prop_id that represents the AxysNum field. Then once you have those seven documents, use the Client to set a value on AxysNum, save the change, clear out the value, save it again, and that should address the matter.

There are probably other ways that handle this better, but that's one way that might take the least effort.