I don't know if this helps, but I gave Sierra a hat and she wore it for a week and then it just disappeared. The other accessories I gave her are still on her (hasn't been a week yet for them) but the hat is gone after a week. Maybe they only wear what you give them for one week?
When I gave James his Wind Cape, his Hatchimaki went away, and now there isn't ANYthing on his head... I'm starting to wonder if it's a limit on how many things they're wearing, rather than what they are. I'm about to do some testing. I'll get back to you with my results.