The amsxport.bst style file does not exist. As far as I remember, it has been dropped years ago (there's no trace of it in TeX Live 2012). In its place five styles called amsrn, amsru, amsra, amsry and amsrs are provided.
All five styles have
FUNCTION {format.title}{
duplicate$
missing.or.empty
{ pop$ "" }
{ "t" change.case$ }
if$
}
which means that the title is made lowercase. This is the house style of AMS.
By the way, a \bibliographystyle declaration in a document loading amsrefs does nothing at all. The choice among those styles is done via package options.
What can you do?
Find amsrn.bst in your TeX distribution; copy it under a new name in the same directory as your test TeX file
Modify the function format.title reported above so that it becomes
FUNCTION {format.title}{
duplicate$
missing.or.empty
{ pop$ "" }
% { "t" change.case$ }% removed!!!!
{ }% added!!!!
if$
}
Modify your test file to be
\documentclass{article}
\usepackage{amsrefs}
% override amsrefs style selection
\makeatletter
\def\bibtex@style{amsrn-mod}
\makeatother
\begin{document}
\nocite{*}
\bibliography{references}
\end{document}
Now run LaTeX and BibTeX as usual.
The references.bib style I used is
@book{a,
author={A. Uthor},
title={A Capitalized Title},
publisher={Pub. Lisher},
year={2000},
}
@book{b,
author={A. Uthor},
title={An uncapitalized title},
publisher={Pub. Lisher},
year={2001},
}
@article{c,
author={A. Uthor},
title={A Capitalized Title},
journal={Journal},
year={2002},
}
@article{d,
author={A. Uthor},
title={An uncapitalized title},
journal={Journal},
year={2003},
}
The produced .bbl file is
% \bib, bibdiv, biblist are defined by the amsrefs package.
\begin{bibdiv}
\begin{biblist}
\bib{a}{book}{
author={Uthor, A.},
title={A Capitalized Title},
publisher={Pub. Lisher},
date={2000},
}
\bib{b}{book}{
author={Uthor, A.},
title={An uncapitalized title},
publisher={Pub. Lisher},
date={2001},
}
\bib{c}{article}{
author={Uthor, A.},
title={A Capitalized Title},
date={2002},
journal={Journal},
}
\bib{d}{article}{
author={Uthor, A.},
title={An uncapitalized title},
date={2003},
journal={Journal},
}
\end{biblist}
\end{bibdiv}
where you can see that titles are as input in the .bib file.
\documentclasscommand, have a minimal preamble and then\begin{document}...\end{document}. The code should compile and be as small as possible to demonstrate your problem. Cutting your code down to a MWE may well reveal what your problem actually is. In any case, it is really difficult to help you without more information. – Oct 21 '16 at 00:55