For the past 2 or 3 days, this guy here http://beastkeeper.com/pet/1008628 has been stuck in exploring an island mode. I tried to do a few exploring rounds on my phone with him, it lagged so badly that I gave up. When I logged back in from desktop, there he was, still on the island.

I've tried logging out and logging back in, I've tried clearing my browser's cache, nothing's fixed it. Help!

Is the Explore feature still lagging, or are you able to move him around on the island? You might already know this, but in case you don't: a pet doesn't automatically exit Explore when you log out--they'll just stay there until you walk them to the portal and leave the island. 

I didn't know that! Thank you, that fixed it.