I have never had this problem before. Often while editing and playing the timeline the playback cursor stops at the end of a videoclip and won't play on. Why?
If you have the program set not to loop on playback within the program and use the [>] playback button rather than the normal > playback button and the range markers are only set to cover the first clip, then the playback will stop at the end of the first clip.
There could be other reasons I'm not aware of if you use keyboard shortcuts.