have you cut the video stream without re-encoding it? You might check your group-of-pictures settings.
I only know this effect when cropping some seconds at the beginning of videos: When the first I-Frame is cropped, the video-stream only appears after the next I-Frame - this can take many seconds...
You might want to check the framerate of your video and the one of your composition and match it.
If they don't match the app will try to fill the timeline of the composition with footage that is 'shorter' in terms of frames per seconds.