Amsart has a curious behavior: if a subsection title is empty, its number is bold. This is achieved by the following lines inside \sect definition:
\@ifempty{#8}{%
\ifnum #2=\tw@ \def\@secnumfont{\bfseries}\fi}{}%
Here #2 is the section level (1 for section, 2 for subsection, 3 for subsubsection etc).
So what you need is to take out the check whether title (#8) is empty, and subsection number will be always bold.
This does the trick (I just took the amsart code and deleted \@ifempty check):
\makeatletter
\def\@sect#1#2#3#4#5#6[#7]#8{%
\edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}%
\ifnum #2>\c@secnumdepth \let\@secnumber\@empty
\else \@xp\let\@xp\@secnumber\csname the#1\endcsname\fi
\@tempskipa #5\relax
\ifnum #2>\c@secnumdepth
\let\@svsec\@empty
\else
\refstepcounter{#1}%
\edef\@secnumpunct{%
\ifdim\@tempskipa>\z@ % not a run-in section heading
\@ifnotempty{#8}{.\@nx\enspace}%
\else
\@ifempty{#8}{.}{.\@nx\enspace}%
\fi
}%
\ifnum #2=\tw@ \def\@secnumfont{\bfseries}\fi
\protected@edef\@svsec{%
\ifnum#2<\@m
\@ifundefined{#1name}{}{%
\ignorespaces\csname #1name\endcsname\space
}%
\fi
\@seccntformat{#1}%
}%
\fi
\ifdim \@tempskipa>\z@ % then this is not a run-in section heading
\begingroup #6\relax
\@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
\endgroup
\ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
\else
\def\@svsechd{#6\hskip #3\@svsec
\@ifnotempty{#8}{\ignorespaces#8\unskip
\@addpunct.}%
\ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
}%
\fi
\global\@nobreaktrue
\@xsect{#5}}
\makeatother