#1 problem in this case is always rider error. the 1st-2nd shift is by far the worst one as u need to literally skip over neutral inside the gearbox. if u dont pull up on the shift lever w/ the correct timing, enough force, and most importantly enough distance... ull miss it. my best suggestion, other than working on smooth shifting, is to adjust your shift lever properly (move it down for starters). get it to a good feeling position within the range of motion of your foot so u can mesh those gears.
sadly, if none of this works... it may be a mechanical issue. currently doesnt sound like one, but if the bike starts to pop out of 2nd gear when on the throttle u may have a worn shift drum or a bent shift fork. however, assume this is NOT the case as it is rare to actually have a mechanical problem, esp on a Honda. maybe if u were riding an older gen R6... 
Naked 93' F2...... RIP -- 04/12/07
04' 600RR Black - currently stuck between track and street usage
- Brembo Master, Sato's, & Ohlins out back