If a toolbox in ArcMap or ArcCatalog is created within the ArcToolbox Window, the next time the application is opened, the toolbox is not listed.
The custom toolbox was not saved.
Solution or Workaround
Right-click in empty space anywhere within the toolbox and select Save Settings > To Default.
This saves the toolbox reference to the default template; the normal.mxt for ArcMap and the normal.gxt for ArcCatalog.
As an alternative, the toolbox settings, including any custom toolboxes, can be saved to a file and loaded on demand, instead of saving to the default template.