Remember how Terence cleans up Tinker Bell's work station while she's still working, indicating that he's a Neat Freak? Of course Terence would be a Neat Freak - he's a dust-talent sparrowman, and every speck of fairy dust is precious and cannot be left loose.
In Fairy Haven & The Quest For The Wand, the fairies have to get a wand to the mermaids to save fairy haven. Now, remember how Disney often portrayed Tinker Bell with a magic wand despite the fact she never had one in the movie? Nice one, Gail.
In The Great Fairy Rescue, Lizzie's father consistently denies the existence of fairies, trying to get his daughter to believe that they are not real. As we've seen in Disney movies before (and the original Peter Pan) a fairies suffer a terrible fate when met with disbelief, leading to some unfortunate implications...
Wasn't that only with children?
It only seems to happen when said directly to them. If fairies died everytime someone didn't believe in them (with-or-without saying so), they probably wouldn't be as numerous.
Nope, any fairy could poof and disappear at any time due to disbelief. If it makes you feel any better, I always assumed if the child transitioned from child to adult without saying "I don't believe in fairies," the fairy would be safe, more or less (as well as assuming you could only kill "your" fairy, as in the one that was created due to your first laugh).
You know the incomplete fairies, the ones that the rest kind of look down on? They're the fairy equivalent of the disabled...