yea hi there, ive had a similar problem, when your out racing you tend to wind the throttle open a bit more and quicker than you do when your just riding around home because your under pressure, you give it gas expecting to go harder, but when your at home riding you open up the throttle slowly and the bike picks up no prob, try to keep the bike over 3\4 throttle cause thats where 125s get there power, its a 125 your meant to rev the heck out of them, but you should also make sure your air filter is clean you carb is clean and jetted properly your reeds are in good condition, your engine must be in good condition, check your crank seals piston and rings measure bore make sure the gasgets are doing what there supposed to be doing your plug must also be good, clean your power valves decarbonize every thing thats gets carbonized, repack your silencer and check to make sure your electrical system is in good condition, check its resistance etc, make sure your clutch is not slipping you fibers could be worn, use good gas and oil, if you check all of that then your bound to find the problem and more, your bike will run like new if you do check everything ive mentioned,
remember a 125 has no power down low so dont expect it to have power when you wind on the throttle, KEEP IT SCREAMING