I was befuddled by this for a long time.
Alert sounds would just stop making noise. This includes dings from txt messages and new mail.
If I went to Settings>Sounds>Text Tone and select several options, all I would get were vibrations.
I rebooted the phone and toggled the silence switch on and off.
I finally figured out that if I started a game and turned the volume up, the noises would come back.
I think it is reasonable for a user to wish to play a game on mute but still hear alert messages.
I think if we can only have two separate systems for audio control, the alert sounds should be tied to the ringer, not to the media/game sounds.
When I spoke to an apple support person over online chat, they seemed to agree that this sounds like a bug.
I have seen many confused posts in these forums regarding alert sounds suddenly disappearing.
Below is the text that I submitted at http://www.apple.com/feedback/
If you share this problem, I suggest you do the same.
My case number is 606343836
I've had a 5S since a few weeks after launch and this problem has only come about in the last few weeks, so I suspect it has to do with a recent OS patch.
Sometimes my alert messages just stop working. They seem to work one minute, then they stop. Alert messages would include email notifications and txt message pings. When they are not working, I can go into Settings>Sounds>Text Tone, and all of the options will simply result in a vibration and no sound.
Rebooting the phone does not fix the problem.
What I have found to fix the problem is to open a game and raise the volume of the game. Then when I exit the game, alert messages start again.
This seems reversible, if I go back in and mute a game, my alert messages go away as well.
If this is by design, I do not think it should be, as I think it is reasonable for a user to want to control the "media" part of the volume separately from the "ringer" and "alerts" part of the volume. It makes sense to want play a game or video on mute but still get alert messages. If anything, I think the alerts volume should be tied to the ringer volume, I think that would make sense.