This is inspired by Re-displaying section headings after page-breaks
We define a new bibheading that repeats the chapter heading on each following page with \EveryShipout. We need to clean up the code after the bibliography, this is what the redefinition of \blx@endbibliography does.
MWE
\documentclass[12pt, a4paper, oneside]{memoir}
\usepackage{lipsum}
\usepackage[style=authoryear]{biblatex}
\bibliography{biblatex-examples.bib}
\usepackage{everyshi}
\makeatletter
\defbibheading{contbibnumbered}{%
\chapter{#1}%
\gdef\@cont@heading{%
\if@twocolumn
\@topnewpage[\@makechapterhead{#1 (continued)}]%
\else
\@makechapterhead{#1 (continued)}%
\fi
\@afterheading
}
\EveryShipout{%
\ifdim\pagetotal>\pagegoal
\aftergroup\@cont@heading
\fi%
}%
}
\def\blx@endbibliography{%
\csuse{blx@endenv@\blx@theenv}%
\global\let\@EveryShipout@Hook\@empty%
\blx@noitem
\endgroup
\blx@bibnote\blx@thepostnote
\endgroup}
\makeatother
\begin{document}
\chapter{Deneme}
\cite{worman,geer,sigfridsson,knuth:ct:a,knuth:ct:b,knuth:ct:c}
\lipsum[1-10]
\nocite{*}
\printbibliography[heading=contbibnumbered]
\chapter{Deneme}
\lipsum[1-10]
\end{document}
\defbibheading{bibliography}is useless since it appears after the bibliography, so it does not change anything. – moewe Nov 15 '17 at 14:09