When exploring, traveling long distances, moving at high speed (ice  boat), or traversing portals Pet Cats become lost.  Have not tested Eletra.  They also displace nether portals when following you through.  (Player returns to original portal, cat spawns new portal, which henceforth player travels to until destroyed.)

Suggested solution:  Pets should always respawn near player when despawned, or exceed a set distance.  Adding a reusable item, (flute-whistle??) would summon pet to player.  Also these animals should not be dying.  Going through the time to tame, and name your pet, you REALLY don't want them dying for no reason, I mean c'mon guiz...  Likely said whistle would summon animals who die as well.

Thanks, good luck!!