The ccaption package allows for "continuation captions". So to implement what you want, you could do the following (adapted from the ccaption documentation.)
Update
Since you wanted the first table to have a letter suffix as well, I've changed the code to allow two commands: \splittablecaption and \splittablecaption*. This also removes the need to manually reset the subtable caption counter. Use the starred version for the first in the series, and the unstarred version for any subsequent ones.
\documentclass{article}
\usepackage{ccaption}
\newcounter{splittab}
\renewcommand{\thesplittab}{\alph{splittab}}
\makeatletter
\newcommand{\splittablecaption}{\@ifstar\splittablecaptionstar\splittablecaptionplain}
\makeatother
\newcommand{\splittablecaptionplain}[1]{\stepcounter{splittab}\captiondelim{\thesplittab: }\contcaption{#1}}
\newcommand{\splittablecaptionstar}[1]{\setcounter{splittab}{0}\stepcounter{splittab}\captiondelim{\thesplittab: }\caption{#1}}
% Usage: for a split table, use \splittablecaption*{} for the initial caption
% and \splittablecaption{} for the subsequent captions
% There is no need to reset the counters manually, as this is done inside the
% starred version of the \splittablecaption command.
\begin{document}
\begin{table} \centering \splittablecaption*{A multi-part table} \label{tab:m}
\begin{tabular}{lc} \hline
just a single line & 1 \ \end{tabular} \end{table}
\begin{table} \centering \splittablecaption{Continued} \begin{tabular}{lc} \hline
just a single line & 2 \ \end{tabular} \end{table}
\begin{table} \centering \splittablecaption{Concluded} \begin{tabular}{lc} \hline
just a single line & 3 \ \end{tabular} \end{table}
\begin{table} \centering \splittablecaption*{A multi-part table} \label{tab:m}
\begin{tabular}{lc} \hline
just a single line & 1 \ \end{tabular} \end{table}
\begin{table} \centering \splittablecaption{Continued} \begin{tabular}{lc} \hline
just a single line & 2 \ \end{tabular} \end{table}
\begin{table} \centering \splittablecaption{Concluded} \begin{tabular}{lc} \hline
just a single line & 3 \ \end{tabular} \end{table}
\end{document}
\end{document}had no newline after it) and that appears to have fixed it. I'll see if this has been reported on meta.SO. – Andrew Stacey Jan 26 '11 at 21:21