I've been having the same problem on my HTC 8X since the last software update (I believe I downloaded that somewhere between November and December), down to having to restart the phone in order to get the sound back for whatever period of time it deems me worthy of enjoying it. Can't say I've found a way to solve it, although I've been thinking about reverting to the factory settings to see if that helps.
It wouldn't be so bad if it was just the sound disappearing, but it's not just being unable to listen to music. Doodle Jump flat out crashes when it fails to play the jumping sound in the menu, and YouTube refuses to play videos, telling me it can't be done on this device. Worse yet, I'm having trouble talking with people over the phone, as all the speakers seem to die out completely; I can't even hear the calling sound, even though my call is indeed getting through and people can hear me on their end.
And yes, restarting solves all these problems - temporarily.
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