I have an SGS3, and the text message tone kept getting cut short. I have the default ringtone on it, because I'm too lazy to switch it over to something else, and it'd play somewhere between a single note and half the ringtone before stopping. This was irritating, obviously, so I went searching for a solution. I found one over at the samsung galaxy s3 forum, by user agentstavros (post #14)
"In the message setting, there is an option to automatically delete messages after a set number. If the conversation is at its limit, when you receive a message, the phone tries to delete the oldest message in the conversation, cancelling the notification. Deselect the check box, and your notifications should play properly again."
Works for me, now my entire sms tone plays.