When I leave the on arena I sometimes fall through my island and die and lose my loot quite a bit why does this keep happening
Its just a glitch. It happened to me a few times and all I could do to stop it was type /home as fast as I could. I only survived because on my island I spawn in water, but if you die with your things don't worry because when you respawn you get it all back.
I think he is trying to say he falls right through his island to the void... I would sometimes do /home and end up in the lower part of my island below my bedrock and would have fell to the void if I didn't have a lower layer. I would say your best bet to not fall to the void would be to have platform about 5 or 6 blocks below your bedrock to work as a safety net for you to land on if you do keep falling through your island.
I've done a platform a bit under my island and It'll be hard to break all of it and I still fall through it sometimes