I managed to get Fazril's axe back from my first two deaths (thankfully, since they were both caused by bugs). Wasn't until I died on north road with my recall point as Arkham that I failed to get back to my corpse in time.

Also, there are good reasons not to sacrifice an APs axe. I kept Harokatsu's so I could give it to another AP to leech. However, there are also tactical reasons to keep an AP's axe, for future fights against them.