I see this issue a lot, and usually it's tied in with another issue where the volume keys on the side of the iPhone will not adjust the volume from the home screen. The volume icon will show up on the screen when you push the buttons but it won't adjust, but during phone calls or when playing back a voice recording, the volume buttons work fine. This issue also causes music not to play from the speaker. The issue is ALWAYS the dock-connector in my experience. Either clean it or replace it if that doesn't work.
*Note: If you want to test to see if this is the issue, remove the back of the iPhone and while it is still powered on, remove the 2 screws securing the dock connector flex, and unsnap it from motherboard. Now test the volume keys from the home screen. If it works now, you know your issue lies in the dock connector.