I think I know why my PDF, at least, has conversion problems. It has a font called "Charis SIL" embedded, and is something called a "smart font"
Charis SIL is a TrueType font with “smart font” capabilities added using the Graphite, OpenType®, and AAT font technologies. This means that complex typographic issues such as the placement of diacritics or the formation of ligatures are handled by the font, provided you are running an application that provides an adequate level of support for one of these smart font technologies. With the old font (and its derivatives), diacritic placement was handled using non-standard character encodings that incorporated multiple versions of a diacritic as distinctly-encoded characters.