\vspace in beamer

Put empty lines (aka paragraph breaks) before and after the tabular.

\documentclass[t]{beamer}

\usecolortheme{rose}
\begin{document}

\begin{frame}{Results: School children}
    \begin{block}{Hypothesis}
        School closures may cause significant reductions in disease spread
    \end{block}

    \begin{block}{Results}
    Worst case scenarios:

    \bigskip
    \begin{tabular}{|c|c|c|}
\hline \textbf{\% School Closure} & \textbf{Clinical Attack Rate} & \textbf{Mortality per 100,000} \\ 
\hline 0 & 30.6\% & 614 \\ 
\hline 100 & 0.6\% & 4 \\ 
\hline 
\end{tabular}

    \bigskip
    With 100\% school closure starting early (0.1\% of population symptomatic) mortality is reduced \textbf{below normal levels for US seasonal flu}

    \end{block}
\end{frame}

\end{document}

In general, make sure you have a new line before the \vspace (or \bigskip) command, for instance:

This won't work:

    Worst case scenarios:
    \vspace{1cm}
    \begin{tabular}{|c|c|c|}

This will:

    Worst case scenarios:

    \vspace{1cm}
    \begin{tabular}{|c|c|c|}.

If you don't want to break a paragraph, you can use \\[size]

...
\begin{block}{Results}
Worst case scenarios:\\[2ex]
\begin{tabular}{|c|c|c|}
....