If your video and audio is not either "combined" or "grouped" when you cut and move the video object, the audio object will stay where it is.  If you move your video object and the audio does not travel with it then out of sync problems can happen. 

Try opening a fresh project (a short one) and importing a video clip with audio.  You should see only one track (default).  Make two cuts  about 3 seconds apart, remove 3 second section, and then squeeze the two parts togther.  Did the out of sync problem happen?  If so, you have a problem I can't help you with.

Open another fresh project. Import your video with audio.  R-click on the video and then select audio functions.  Choose place video and audio on seperate tracks.  What this does is put the audio and video on diffrent tracks but they are still grouped.  Peform the seme experiment and you should receive the same result.

Last, fresh project,  sperate the video and audio.  Then click the ungroup botton.  Its to the left of the mouse mode arrow.  When you do this you should be able to select the video and audio seperately.  Make a 3 second section in the video portion like above and remove the portion.  Your video stream should have a gap in it.  Your audio should still be whole.  Now move the video steams together.  Your audio and video should now be out of sync the minute you hit the spot with the section ripped out.