The first page of the references chapter is usually set in page style plain, therefore the new headers can already be set at the start of the bibliography. Simplified example (the class PhDthesisPSnPDF is based on report) with the bibliography given explicitely,
it should also work with using the .bbl file.
\documentclass[twoside,12pt]{report}
\usepackage[a6paper]{geometry}%
\pagestyle{headings}
\makeatletter
\newcommand*{\ORG@thebibliography}{}
\let\ORG@thebibliography\thebibliography
\renewcommand*{\thebibliography}{%
\cleardoublepage
% without uppercasing
% \markboth{References (Continued)}{References (Continued)}%
% with uppercasing
\markboth{\MakeUppercase{References (Continued)}}%
{\MakeUppercase{References (Continued)}}%
% disable the header setting of the original thebibliography
\let\@mkboth\@gobbletwo
\ORG@thebibliography
}
% Clear the header after the last page of the bibliography
\let\ORG@endthebibliography\endthebibliography
\def\endthebibliography{%
\clearpage
\markboth{}{}%
\csname ORG@endthebibliography\endcsname
}
\makeatother
\begin{document}
\begin{thebibliography}{9}
\bibitem{2010} First.
\newpage
\bibitem{2011} Second.
\newpage
\bibitem{2012} Third.
\end{thebibliography}
\cleardoublepage
After references.
\end{document}

\markboth{References (Continued)}{References (Continued)}just before the first entry in the bibliography. you may have to go into the.bblfile to do it; that would get wiped out if you have to reprocess from a.bibfile, but it should do the job. – barbara beeton Sep 06 '12 at 21:20