Being a sintered diamond, the entire tip of the core drill has diamond impregnated through it. When it begins to wear down, it simply means that the topmost layer of diamond is used up and the diamond beneath it has not been exposed yet.
Just use a dressing stick and drill two or three times into the stick. This will strip off the layer of metal holding the older worn diamonds and expose brand new diamonds underneath.
Your drill should work like new again.