Based on the fact that there hasn't been any mods, I'd say that what you're running into has more to do with the rake and trail as designed by the manufacturer, rather than any malfunction or failure. That said, there are mods you can do to change the bike's characteristics if you so choose, although I'd recommend a new question for that.
The bike's desire to stand upright is wholly dependent on the rotating mass of the tires and wheels. Lighter wheels (common in racing) allow the bike to be more nimble, and make it easier to "flick" around. Heavier wheels make it harder to flick, but make it much more stable in a straight line.
Just like the weight, the speed at which the wheels are rotating affects the bikes natural desire to stand up. So you'll notice that the bike will be more willing to dive downward when you're going slow, than when you're moving quick. This also directly affects the amount of force you have to exert to steer/countersteer since you're essentially fighting gravity.
Basically, you're wheels act just like a gyroscope (don't know if you ever had one of these to experiment with, but there are plenty of videos on the web if you don't know what I'm talking about). The faster they're spinning, the more stability they have to fight gravity and help you move them around. The slower, the more they will be affected by gravity.