It should not be that tough to screw in. If it comes to needing that much strength, then you should unscrew the screw, drill a bigger pilot hole as deep as the screw is long, and try again. When drilling the pilot hole, you will find out if the remains of another screw is still in the hole in which case you may need to relocate the hinge.
I'm with Alan. It sounds to me like your screws are hitting the bottom of the previous screw hole and are refusing to dig into the solid wood. Get a drill bit that's at least 2" and drill those holes a little deeper.
My next question... and don't be insulted... it is a screw thread, after all : You do have 2" of material to screw into, right? I mean, it's not a 1/2" stud w/concrete behind it, is it?