Yes, the hat stays on - most of the time.
Soren was in need of more diapers, so even it would have been so nice to stay home him and me took off to run errands and a trip to Walmart. While passing the baby section we saw that there were new hats and he did get to try them on. Soren was not really happy about the idea and of course kept pulling them off, but most of them were falling of anyway. The hats only come in one size and are already for toddlers, but believe me he does have such a big head that the infant size is joke. And for the rest of our shopping tour through the store he kept the hat on, too. Now I have to get used to keep looking for the hat, too, after sock one, sock two, pacifier, blanket, toy one, toy two, tea bottle, ... for pretty much everything that we take out of the house including baby.
Leland already had to crawl under my car to get that hat back out. LOL