Yip this is an occurring issue with Samsung handsets, its pathetic and they obviously don't know how to fix it !

My Galaxy S3 has this problem now and then and nothing I do nor the work arounds people mention ever seem to fix this.

Theres been a couple of threads already on the issue:

http://androidforums.com/samsung-galaxy-s3/561283-notification-sounds-cut-off.html

http://androidforums.com/samsung-galaxy-s3/581369-notification-audio-vibrate-glitches.html

 

Yeah i've changed my notification to a few different things and had the same issue with all of them.

 

I was having a similar problem. I did a little research and found out that the app ChatOn was causing the problem. I shut down that app and rebooted my phone and have had no further problems.

 

This was going to be my question to you.

Have you installed any other new apps SINCE you have noticed this happening? There might be a conflict in the MediaStream that tells the phone to play a notification sound that is causing yours to be cut off.

 

My phone started doing this today. I have no third party apps associated with the notification tone.
Will be watching this thread with interest for a solution.

 

I noticed that with mine as well. I thought that maybe it does that because the proximity sensor sensed that someone was near so cut off the sound? Just speculation really