Just wondering how much of the tool steel inset is visible? Might be a possibility that the axe head has been used so much that it has exhausted the tool steel insert, and the mild steel that comprises 90% of the head has now reached the cutting area
Another possibility is that the axe has been stored in such a way that it came in contact with the ground for an extended period of time, this will draw the temper out of the tool steel
If that is the case, and there is still lots of tool steel visible, you should be able to have it re tempered by a local blacksmith or a good machinist, using a tempering guide in an old mechanic's manual
The trick will be to not get the tempering too hard so that the steel becomes prone to failure along the cutting edge
It is a little easier to control the tempering using today's technology, in yesteryear the blacksmith if they were good could watch and follow the color pattern in the steel as it cooled and hardened--I have had some old tools re tempered by our resident blacksmith George York over the years it was great to watch him work steel, he could just about do anything, or make anything or repair anything you needed in the restoration field
We were working on an 1865 Carding machine one time and it was then I was introduced by George to the different bolt threads used at that time, but that is for another discussion