I was having the same problem a few years ago as well. The problem was solved for 75% when I used a SHARP axe. A high quality sharp carpenters axe is completely different from a $5,- hatchet you can buy at any hardware store, but which you can never get sharp enough. A sharp axe makes the work so much better. I can now work for an hour with the axe, without having serious pains or cramps. I get blisters before my lower arm feels like a balloon ready to pop.
Another 15% was solved by using a lighter axe. An axe weighting 1½ pounds is much, MUCH more tiresome than a 1 pound axe.
The last 10% was solved by a combination of improved technique and increased muscle strength in my lower arm. The first time I used the axe, my muscles were not yet completely developed, but after a few times my muscles became used to the motion.