Far more often than you'd think, one of your tools ends up in:
The Fridge
Your Chests, anywhere on the map
The AutoGrabber
Junimo Hut??
any other place I'm forgetting that can hold a tool
but the Refrigerator is the leading unintentional stealer of missing tools and yes, I found my Axe in there once after it went missing.
Edit: Which makes me wonder if Robin looked in there first before sending you on the Lost Axe quest in early game. OK now I want a mod where you can just tell her to check the Fridge and about 20% of time she finds it in there!