The captions are already defined by the ieee.cls
. Hence the captions can not be defined by the subfig
package. You should use caption=false
as the option for subfig
package.
\documentclass[
final,
reprint,
notitlepage,
narroweqnarray,
inline,
twoside
]{ieee}
\newcommand{\latexiie}{\LaTeX2{\Large$_\varepsilon$}}
%-----------------------------------------
\usepackage{epstopdf}
\usepackage[caption=false]{subfig} % <---------------------changed here
\setlength{\captionwidth}{\columnwidth} %<-----------------Add this to correct table captions
%-----------------------------------------
\begin{document}
\begin{figure}
\centering
\subfloat[one]{\label{fig:one}\includegraphics[width=.4\textwidth]{figures/one.png}}
\hfill
\subfloat[two]{\label{fig:two}\includegraphics[width=.4\textwidth]{figures/two.png}}
\caption{some text representing the caption of the current figure properly}
\end{figure}
%--------------------------------------
\begin{table}[!t]
\centering
\renewcommand{\arraystretch}{1.3}
\caption{a caption displaying OK}
\begin{tabular}{|c|p{2.5cm}|p{2.5cm}|}
\hline
&Average distance (km) & Total distance (km)\\ \hline
set 1&5.137&102.749\\
set 2&1.602&32.058\\
\hline
\end{tabular}
\label{tab:distances}
\end{table}
%--------------------------------------
\end{document}
Edit: The ieee.cls
provides a length \captionwidth
. You can define it to be column width like \setlength{\captionwidth}{\columnwidth}
so that table captions are fixed. I have modified the above code accordingly.

Short answer:
Switch to the subcaption
package.
Long answer:
The problem comes from a bad interaction between the H
placement specifier from the float
package and subfig
, as the following reduced example shows:
\documentclass[a4paper]{scrreprt}
\usepackage[demo]{graphicx}
\usepackage{float}
\usepackage{subfig}
\begin{document}
\begin{figure}[H]
\centering
\subfloat[test]{\includegraphics[width=3cm]{image1}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image2}}
\caption{First part of a continued float}
\end{figure}
\begin{figure}[H]
\centering
\ContinuedFloat
\subfloat[test]{\includegraphics[width=3cm]{image3}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image4}}
\caption{Second part of the continued float}
\label{dr:s:ist:som}
\end{figure}
\begin{figure}[H]
\centering
\subfloat[test]{\includegraphics[width=3cm]{image5}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image6}}
\caption{Another independent figure with subfigures}
\label{dr:s:ist:win}
\end{figure}
\end{document}

Removing the H
placement specifier fixes the problem with the subfigures, but creates another one:
\documentclass[a4paper]{scrreprt}
\usepackage[demo]{graphicx}
\usepackage{float}
\usepackage{subfig}
\begin{document}
\begin{figure}
\centering
\subfloat[test]{\includegraphics[width=3cm]{image1}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image2}}
\caption{First part of a continued float}
\end{figure}
\begin{figure}
\centering
\ContinuedFloat
\subfloat[test]{\includegraphics[width=3cm]{image3}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image4}}
\caption{Second part of the continued float}
\label{dr:s:ist:som}
\end{figure}
\begin{figure}
\centering
\subfloat[test]{\includegraphics[width=3cm]{image5}}\quad
\subfloat[test]{\includegraphics[width=3cm]{image6}}
\caption{Another independent figure with subfigures}
\label{dr:s:ist:win}
\end{figure}
\end{document}

Now, the subfigures are correctly numbered, but figures are not. The definitive solution is to switch to the subcaption
package (you can even use again the H
specifier). In the following example I used \subcaptionbox
, but the package offers also a subfigure
environment:
\documentclass[a4paper]{scrreprt}
\usepackage[demo]{graphicx}
\usepackage{float}
\usepackage{subcaption}
\begin{document}
\begin{figure}[H]
\centering
\subcaptionbox{test}{\includegraphics[width=3cm]{image1}}\quad
\subcaptionbox{test}{\includegraphics[width=3cm]{image2}}
\caption{First part of a continued float}
\end{figure}
\begin{figure}[H]
\centering
\ContinuedFloat
\subcaptionbox{test}{\includegraphics[width=3cm]{image3}}\quad
\subcaptionbox{test}{\includegraphics[width=3cm]{image4}}
\caption{Second part of the continued float}
\label{dr:s:ist:som}
\end{figure}
\begin{figure}[H]
\centering
\subcaptionbox{test}{\includegraphics[width=3cm]{image5}}\quad
\subcaptionbox{test}{\includegraphics[width=3cm]{image6}}
\caption{Another independent figure with subfigures}
\label{dr:s:ist:win}
\end{figure}
\end{document}

The demo
option for graphicx
simply replaces actual figures with black rectangles; do not use that option in your actual document.
Best Answer
For the subfig package see sections 2.2.2 and 3 of the documentation.
(Original answer)
Assuming you're using the subfloat package, section 4 of its documentation indicates you can do something like:
to put the sub-number in parentheses.