I'm not 100% certain about this being a bug but I heard people saying that tamed horses should not despawn, although it is happening, and even with named horses. that does not only affect horses but donkeys and mules as well. the saddles and armors on horses are disappearing too. but lucky for us llamas are safe.

this bug affects the current version of the bedrock edition. I play on ps4 so i am not sure about other platforms. I'm sorry for bothering you if this was not a bug and thanks for all your efforts to make Minecraft better.