I have a 2005 plate CBR125R and it runs fine, except it has a tendency to stall when slowing down just before stopping (eg. at traffic lights). It was also idling unevenly, but I tweaked the idle screw and sorted that problem. It’s fine if I hold the revs around 2000 whilst sitting still but if not the revs slowly drop until it dies.
cbrgaz, MCN forums
It sounds like your pilot jet is partly blocked. This jet works mostly up to 2000rpm. A possible cause could be rust from the fuel tank is flowing through the fuel line to the carb. If the bike hasn’t been used for months, then old fuel could have gummed the jet up a little too. It’s pretty easy to get the carb off and inspect and clean it. You could also fit an inline filter to the fuel line to stop this reoccurring.