Headphones that have an in-line mic have a slightly different connector than the ordinary stereo minijack.
If either the connector on your regular headphones are damaged or the internal socket is damaged, this is a typical result.
The PS Vita is designed to utilize inline mics like cell phones do (their official Vita headphones have an inline mic) but I don't have any problem getting stereo output on my hi-fi 'phones which do not have a microphone built in.
Sadly, the fix is to try another pair of headphones to see if the Vita's stereo minijack socket is damaged, or try a headphone jack splitter (or extension cord) if the headphones in question are valuable (I had a $130 Bose set for like 4 or 5 years before it was unusable, "just replacing them" would have been absurd if a headphone jack splitter or extension cable would have stabilized the connection).
It's weird because the headphones work perfect with other devices. Also, another problem I've been having wth my Vita is that it says it's dead, even though a moment earlier it said it was full, and I can just press the PS button to turn it back on. I'm not sure if using a converter messed it up (because I'm in Italy right now and have a US system).
just to ask, are you trying to use cellphone headphones?? i mean the ones with 4 metal contacts and 3 plastic separations on the plug?? because there are 2 standards for these plugs, most cellphones, Vita, 3DS and IDevices AFAIK uses this configuration:
but SonyEricsson Xperia 2011 line and some Nokia phones interchange the sleeve signal with the ring 2, thus being incompatible with the other configuration, you can test leaving pressed the button on the mic of the headphone(if any), if works as it should then the pins don't connect when it should connect and thus the headphone has the other configuration that the Vita doesn't uses.