I agree, that one looks very worn. Another way of restoring the point is to chuck the needle in a drill motor and secure the drill motor in a clamp or a vise. With the drill motor secured and turning the part, carefully reshape the tip using a clean, sharp single cut flat file. I have made a number of different small turned parts using this method before I got a real lathe. The biggest challenge with this part is that it is worn enough that a number of threads will have to be taken away to restore the point to a taper that closely matches the original. It certainly can be done, though.
-Ben