I have Poweramp installed, but don't fire it up very frequently. This time, I noticed the issue when using the YouTube app, but I've also had it with MX Player Pro and BeyondPod. As such, I don't think it's app-specific.
FWIW, after my earlier post, I checked on a hunch. Recalling at least one review of our phone model that claimed that the internals are more or less identical to the HTC One Mini, I decided to Google "htc one mini speaker." Sure enough, the same issue affects the Mini, too.
This *may* give some weight to our needs for a fix. If the same issue affects both the Desire 601 and the "more or less the same inside" One Mini, then HTC is more likely to address it with a software update - if that's the root of the problem.
But that's just me reaching and hoping. If it's fixed with Kitkat, then it was software. If it's not, then the issue hasn't been recognized by HTC yet, or it's not enough of a problem to throw resources at fixing, or Virgin Mobile doesn't want to fix it (yet?) due to costs, or maybe it was a hardware issue after all. Or maybe something else.
Let's hope on Kitkat....