This may be due to Spin It Again's automatic track detection feature. If you are using the automatic track detection, it's important to preview the beginning and ending of each song to make sure that no track markers were placed in the center of a song. Automatic track detection works by looking for silence and sometimes it can mistake a quiet part of a song for the end of the song.
You can manually adjust the track markers on the Preview & Edit screen by right-clicking on the image of the sound. We've got a tutorial on how to do this on our Spin It Again tutorials page.