Try overlays:
\documentclass{beamer}
\usetheme{Warsaw}
\setbeamertemplate{theorem}[ams style]
\setbeamertemplate{theorems}[numbered]
\begin{document}
\begin{frame}
\only<1>{ \begin{example}
This is a test example
\end{example}
}
\only<2>{
\begin{example}
Continued previous example.
\end{example}}
\begin{example}
Another previous example.
\end{example}
\end{frame}
\begin{frame}
\begin{example}
Another previous example.
\end{example}
\end{frame}
\end{document}
Only I can can't see 1.1 but 1 as you stated in the comments. So you possibly used another code?
No. 2
Saves counter, and sets counter to the saved value. Usage: smyex
is the parent while emyex
is the child which has the same number, until the next use of smyex
. Hope this is what you understand under automation.
\documentclass{beamer}
\usetheme{Warsaw}
\setbeamertemplate{theorem}[ams style]
\setbeamertemplate{theorems}[numbered]
\newcounter{extemp}
\newcounter{restoretemp}
\newenvironment{smyex}{\setcounter{extemp}{\theexample}\begin{example}}%
{ \end{example}}
%
\newenvironment{emyex}{%
\setcounter{restoretemp}{\thetheorem}
\setcounter{theorem}{\theextemp}
\begin{example}%
}{\end{example}\setcounter{theorem}{\therestoretemp}
}
\begin{document}
\begin{frame}
\begin{example}
This is a test example
\end{example}
\begin{smyex}
Previous example.
\end{smyex}
\begin{example}
Another previous example.
\end{example}
\end{frame}
\begin{frame}
\begin{example}
This is a test example
\end{example}
\begin{emyex}
Continued previous example
\end{emyex}
\begin{example}
Another previous example.
\end{example}
\end{frame}
\end{document}
\setcounter{example}{2}
. Everything should work fine.