I use the Armored Eyltra from Better End in the cape trinket slot.

I enchanted it with Mending and Unbreaking, but when receiving XP the eyltra in the slot doesn't get repaired.

When I hold it in the hand it repairs normally as it should.

So maybe this is a compatibility issue of both mods together or this mod has a bug.
Because the elytra repairs itself in the hand or off hand slot, I think the latter is the case.

If you need any further information, let me know :)