So I went to go retrieve the All-American from Vault 34, but when I finally got to the armory, the All-American wasn't in it's designated spot, so I assumed my companion took, it but when I checked his inventory, it wasn't there. If anyone could give me some help or advice on what has happened, that would be awesome.

Never had this problem. Was Veronica's quest active to go snag the pulse gun? Maybe it has to be active for All-American to appear? If not you may want to try, that is only thing I can think of, unless it fell under a table or box, which can try moving stuff around.