Try putting the tip in the head, then whack it with a hammer a couple times (like you'd hit a chisel). That often frees up small fasteners (like philips heads on trim, door sill trim, etc.)
An impact driver also works very well.
And just to be sure, you are using a dedicated Clutch head screwdriver, aren't you? I've known a ton of people who try to get by with a straight blade in the clutch head. That'll make a huge difference.
I'm fortunate, in that I have a 3-screwdrive set of clutch-head drivers (One old Snap-on, two bought new off the truck a couple years ago for a very reasonable price), and an impact driver with a 3/8-drive socket end. The bits I put on it are made for ratchets--and I have one clutch-head screwdriver bit for a 3/8-inch ratchet.
The impact driver has saved my bacon more times than I can count. Most recently, it took care of the philips fasteners on the barn door slides/latches for my '62 Suburban. I'd have been drilling out the old and buying new hardware store fasteners without that impact driver.
-Brad
