String #6 never stops buzzing

Okay so I've gone through three guitars thus far. My first two were both Ibanez GRGR120EX's (the first one in blue and the second one in white). This third guitar is a Schecter C-1 Platinum. I've made sure I'm holding the pick correctly, but I'm not too sure if I'm holding the guitar right. For some reason, I always get buzz on the sixth string. The lightest of touches always causes this. I've been to multiple guitar techs and they've all told me that the action and neck relief are perfectly fine, and that I'm just playing it wrong. No other strings do this. Anyone have any other advice before I rip my hair out?