Does it seem like when you shift, the lever is returning to center? If you can look at the shaft itself, where it enters the engine on the left side, the shaft goes into a shifter shaft cover.
There is a spring in there to return the shifter to the center position as well as a bolt to secure that spring. There are also some other springs, shifter stopper, etc that may have gone south. If after cleaning all the shifter linkages, problems persist, look up the fisch and prepare to remove that left side cover.
I located part of the shifting mechanism on page 5-53 from (the available on line shop manual) for my 07. And yes it can be a shifter fork but checking this mechanism is much easier and a distinct possibility, especialy if the bike hasn't been dogged.....