Six years later and it's still not working. I've tried everything to export a TIF. Sigh.
ArcGIS 10.5 and this problem is still unsolved!? Why?
This sounds relevant: bug NIM003653, dating back to v9.2 (2006), citing upstream limitation of Microsoft GDI sub-system.
The recommended response is to a) increase default printer page size or b) print from ArcGIS Pro instead which doesn't rely on the same export mechanism. Be aware that font substitution fall back does not happen (boxes may show for unsupported characters).
More details in knowledge base article Bug: Picture symbol legend patches, inserted images, and objects fail to draw when exported to PDF, ...
When images or objects (such as JPEGs, BMP files, or Excel spreadsheets) are inserted in an ArcMap layout with a page size that is larger than the default printer's default page size, they fail to draw or draw incorrectly when exported. Picture marker symbols, or areas with a picture fill, may also fail to render properly on export. Legend patches of web map service layers may become pixelated or fail to draw on export, as well.
Note: At ArcGIS version 9.2 and later, picture marker symbols that are converted to vector with the 'Vectorize layers with bitmap markers/fills' option may also fail to render properly outside of the default printer's default page size. Additionally, certain cartographic representations that draw as an inserted EMF can also be affected by this issue.Cause
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 output.
One workaround is to 'import Map' to ArcPro and 'Share' > Layout to pdf. This worked well for me. I noticed slight change in some of the inserted picture dimensions. otherwise it worked out well.
For anyonbe still looking, I've had some success running the following script from ArcCatalog with ArcMap closed, to convert the .mxd to PDF...