I had read on another board that a lady always had some new insulin syringes on hand because she was getting dull needles all the time. You can easily pick them up at most pharmacies or online (amazon has them around $13-18.00 for 100, depending on the size needed) and there cheap.

I think the lady said with the cap still on the needle pull the plunger out and squirt the med into the new syringe, replace the plunger, turn the needle pointing up, take off the cap and push out the air until the med is at the needle.