So you said you have tried different headsets, different signal sources, but just one converter box. Most likely your super cheap VGA to HDMI converter has fried your headsets. Cheap ebay electronics is not always certified, and many manufacturers skip HDMI certification because royalties are much higher than the profit that they are going to make. This means that most likely nobody has ever tested that box over long duration of time.
Since the box is not guaranteed to follow HDMI specification, it can do something like output a signal with incorrect voltage level. The HDMI inputs are usually protected, but voltage protection is usually implemented as reverse diode, so it degrades very quickly under breakdown voltage (when it is triggered by high voltage). This can explain why it started flickering first and eventually stopped working.