After Effects won't consistently stop previewing video when I ask it to
When you press space bar, After Effects tries to playback the composition out of the current playhead position instantly. Theoretically the playback depends on your machine, but an instant playback of a  composition (in real time) is a very computing-intensive process and with conventional computers not possible at the moment. This also is the simple reason why After Effects sometimes does not respond. Also see the official Improve performance manual.



For correct playback (25fps) use the RAM-Preview instead of the space bar. Press Numpad 0 or the associated |||> in the Preview Panel to start the preview rendering process:




Press Numpad 0 again to stop it
Press Numpad 0 twice to stop and playback the previously rendered (green) frames


In order to facilitate the work:


Set the rendering resolution of the view to a lower value for e.g. to half or quarter
Limit the work area in your timeline, press B to set the start render point (Begin), press N to set the end point (End) 
Enable loop preview (7th button) to repeat the preview of the current work area
Press Numpad ,  for audio preview only