The symptoms that you describe seem to be those of Bug NIM003653 which is discussed in Knowledge Base Article 30753 (Picture symbol legend patches, inserted images, and objects fail to draw when exported to PDF, EPS, AI, and SVG).
See that Technical Article for full details but the key information is:
If the inserted object, image, or legend patch falls outside the
default page size of the Windows default printer, Windows GDI drawing
calls used by ArcMap may not properly draw the object or image on
On some printers, selecting 'Use Printer Paper Settings' in the Page
and Print Setup dialog box alleviates the problem. See the link in the
Related Information section for more information on how to use the Use
Printer Paper Settings option.
Alternatively, set the Windows default printer's default page size to
a page size as large as or larger than the page layout that is being
exported. For example, if the map document is a tabloid size (17 x 22)
set the default printer's default page size to 17 x 22 or larger
before opening ArcMap.
Further information can be found in the ArcGIS Discussion Forums where an Esri staff member says:
If it is [NIM003653: Picture marker symbols or EMF pictures on the
layout can fail to draw on output.], then this is not going to be
fixed, as it is a limitation of Windows GDI.
It will be interesting to see whether this is an issue with ArcGIS Pro when that is released with ArcGIS 10.3 for Desktop.