I just got a ps2 drum (and game) today and am having the same problems. However, I'm pretty sure that my problem isn't with osu.
In the Windows XP control panel, when I test the controller, it has problems registering hits there as well. This tells me that the problem is either with the drum itself or with the adapter. I also need to hit the drum quite hard for it to register at all. It's pretty much useless with the plastic bachi, but using actual wooden bachi, it seems to work a little better (probably not good for the controller, though!)
I might look around for another adapter and see if that helps. I'm currently using some anonymous blue one that has worked pretty well for regular PS2 controllers in the past.
I'll also see if I can try the drum on an actual PS2 to rule out the problem being with the drum itself...
Also, as a note, the GlovePIE script provided in another thread doesn't quite work for me. For me, the left DON is actually mapped to x, not pov1left. More specifically, I used the expression joystick.x < -0.1 Everything else works as is though (of course, I changed the key mappings to match my own).