I'm trying to delete my old shop (DragonStorm/s Cave) and Subeta won't let me do so b/c I keep getting an error message that says I don't own this shop. I'm confused b/c my profile still says that DragonStorm/s Cave is one of my shops (which it was), but when I look at how many shops I have, only 2 are there: an unnamed shop and my shop The Dragon's Cave. My old shop has been deleted on its own, yet still appears on my 'Your Shops' list.

it's likely that it already deleted it and it's just a cache issue. if you wait a bit, it might disappear on its own. you may also want to try a hard refresh and see if that shows it gone.