Anna,
I ran some additional tests from a separate location, PC and even Firefox to see if there was any difference, but was getting the same result initially. I thought it could possibly have someting to do with the infographic being custom - but the map within the Demographic Summary infographic template (Dark Gray basemap) also would not appear on export.
I would however like to revise my answer to number 2 above as I realized the infographic did not depend on the map viewer. When I modified the custom infographic to display either Topographic or Imagery Hybrid basemaps they "stuck" on an export.
So it seems that some basemaps have no issue but some do (including Light & Dark Grey) from what I'm seeing. Luckily in my case credits are not a concern so I can burn them on incomplete exports, but I can see it being a concern for some users.
Anyone else experiencing this?
Thanks