I have the same phenomenon as you, but not only with vocals but a general hissing/noise, especially on the frequencies of the snare or the hi-hat. Could it be that the mechanical components (amplifier, sound membrane, battery) are simply too weak?

I also have the headphones. However, I have not noticed any hissing during singing. I think it's a warranty issue...
If you have any further questions or want to describe the problem in more detail, I will be happy to give you feedback.