This was a story about a young beaver who doesn’t want to die. He encounters a fairy who grants him the wish of immortality but as is characteristic of beavers, he keeps growing through his extended lifespan, loses his friends and family members and outgrows his environment. The denouement escapes me but the essence is his coming to terms with mortality. I hope you can help find it!
Must be The Beaver Who Wouldn’t Die, by Monica de Bruyn.
https://www.amazon.com/Beaver-Who-Wouldnt-Die/dp/069580586X