This is a slightly modified version of Audrey's approach above
\AtEveryCitekey{%
\ifcsundef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}
{\csnumgdef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}{0}}
{}%
\csnumgdef{cbx@instcount@last@\the\c@refsection @\thefield{entrykey}}{%
\csuse{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}}%
\csnumgdef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}{\value{instcount}}}
\def\iflastciteonsamepage{%
\ifsamepage
{\number\csuse{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}}
{\number\csuse{cbx@instcount@last@\the\c@refsection @\thefield{entrykey}}}}
Where \iflastciteonsamepage checks if the last citation of the current work was on the same page (as detected by \ifsamepage).
Please be aware that this test is not guaranteed to work in all circumstances, I have tested it for some (relatively common) cases, but there might well be cases where this breaks down horribly. Thanks to Audrey to pointing this out in the comments.
Audrey's MWE then becomes
\documentclass{report}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[colorlinks]{hyperref}
\usepackage[style=numeric-comp,citetracker=true,pagetracker=true,sorting=none]{biblatex}
\makeatletter
%---------------------------------------------------------------
% Essentially verbatim from Joseph Wright (except for refinements to \ifciteseen test)
% http://www.texdev.net/2010/03/08/biblatex-numbered-citations-as-footnotes/
\DeclareCiteCommand{\superfootcite}[\cbx@superscript]
{\usebibmacro{cite:init}%
\let\multicitedelim=\supercitedelim
\iffieldundef{prenote}
{}
{\BibliographyWarning{Ignoring prenote argument}}%
\iffieldundef{postnote}
{}
{\BibliographyWarning{Ignoring postnote argument}}}
{\usebibmacro{citeindex}%
\usebibmacro{cite:superfoot}%
\usebibmacro{cite:comp}}
{}
{\usebibmacro{cite:dump}}
\AtEveryCitekey{%
\ifcsundef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}
{\csnumgdef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}{0}}
{}%
\csnumgdef{cbx@instcount@last@\the\c@refsection @\thefield{entrykey}}{%
\csuse{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}}%
\csnumgdef{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}{\value{instcount}}}
\def\iflastciteonsamepage{%
\ifsamepage
{\number\csuse{cbx@instcount@curr@\the\c@refsection @\thefield{entrykey}}}
{\number\csuse{cbx@instcount@last@\the\c@refsection @\thefield{entrykey}}}}
\newbibmacro*{cite:superfoot}{%
\iflastciteonsamepage
{}
{\xappto\cbx@citehook{%
\noexpand\footnotetext[\thefield{labelnumber}]{%
\fullcite{\thefield{entrykey}}\addperiod}}}}
\newrobustcmd{\cbx@superscript}[1]{%
\mkbibsuperscript{#1}%
\cbx@citehook
\global\let\cbx@citehook=\empty}
\let\cbx@citehook=\empty
%---------------------------------------------------------------
\makeatother
\addbibresource{biblatex-examples.bib}
\begin{document}
\chapter{Title}
\null\vfill\noindent
First citation.\superfootcite{bertram}
First citation.\superfootcite{companion}
Some recurrent citations on same page.\superfootcite{bertram,companion,augustine}
\chapter{Title}
\null\vfill\noindent
Recurrent citation on different page.\superfootcite{companion}
Recurrent on different page and first citations.\superfootcite{augustine,cicero}
Recurrent citation on same page.\superfootcite{companion}
\printbibliography
\end{document}
For the first page

and for the second page

While this version is more robust in some aspects, it is still not guaranteed to work in all circumstances.