iPhone lock screen/multitasking bar audio controls don't work
Possible Causes:  


Mobile substrate add ons on a jailbroken device  
Corrupt event handling events  
Loss of data with streaming services  
Accessory interference  
Airplay  
Older version of iTunes  


Several things to try:  


If you are jailbroken try booting into safe mode (SBSettings Feature).  
If problem is with data streaming app then try the iPod app.
If accessories are connected, disconnect them.
If the problem persists, restore to the latest version of iOS and update iTunes.