I do a fair amount of center punching. I usually start with a prick punch and then follow that up with an automatic center punch and then maybe a hand punch driven by a 2# hammer if I need a pronounced mark.
My 2 automatic center punches are both exceedingly dull. One is made by Starrett, the other General. Both punch tips are replaceable, and yes, I know how to do that. They use identical threads, maybe 10-32 (haven't measured them) so I could make up a pin with a threaded hole so I could mount the tips in a collet.
Short of a toolpost grinder, is there a good way to repoint the old tips? The ideal way to do it would be to set up the tips in a motorized toolhead on a tool & cutter grinder with a cup stone, but even when I had a T&C grinder I didn't have a motorized toolhead.