I realize I am using a proprietary font here, but this is where I discovered this problem (it also applies to other ligatures as well as old style numbers).
\documentclass{article}
\usepackage{fontspec}
\setmainfont[
Path = M:/MyStuff/Fonts/timesnewroman6.80/,
UprightFont = times.ttf,
Ligatures = Discretionary]{tnr}
\begin{document}
Th
\end{document}

When I copy and paste this from the pdf, on the other hand, I get instead of the expected Th. Looking at how this ligature has been encoded (using FontForge), everything seems to have been done properly:

thas text with my pdf readerokular. Is the font you use publicly available, so we could try to compile the document ourselves? – bodo Sep 13 '13 at 10:06