TLDR - We solved our problem. The prod templates were using URLs to our sandbox file cabinet. We performed a refresh which "deleted" the records in the sandbox causing the broken URLs.
I was using a System Notes search. However, when a record is deleted, the system notes pertaining to that record also appear to be deleted.
I verified this behavior in sandbox by adding a new file to File cabinet -> view system notes in saved search -> delete file from file cabinet -> observe the system notes are gone.