This issue remains unresolved. It only happens to me when I do a short flight, where I have selected "Short Range" on the fuel page in the FS Actions menu. It has nothing to do with the horizontal stabilizer (setting your trim).
I have tried to start on the runway, so the were no external input from the control surfaces whatsoever prior to lining up with the runway. As soon as I advance the throttle the warning sounds until I get the V1 callout, then it goes away.
However, if I take off on a mid range or long range flight (more fuel onboard), it does not happen. I came to the conclusion this might be a glitch in the coding.