Q. If an item for which there is an Appendix is mentioned more than once in a document, should it be noted each time in-text as an Appendix?

If you asking in relation to APA format I would recommend citing the appendix each time. However, the APA Publication Manual does not give precise guidance on this particular issue (or least not any that I can find). While this may be the case, APA style favors clear guidance for the reader to extra information that may be of value so including the extra notation would make sense.