Can drywall harden or become brittle over time? Or, am I dealing with plaster?
If you're hanging curtains I'm going to assume that you are drilling above the window. In that case you've probably hit the lintel.

This will be either a piece of concrete or wood (depending on the construction of the house) designed to spread the load of the wall above the window around the window.

If it's concrete you'll need to use regular rawlplugs in the holes.

If it's wood you can just drill a pilot hole and screw directly into that through the plasterboard.