There was never really a "thing" that I was refused (though I had to wait for some of them), but I think in retrospect that might have been because what I wanted was almost always a book or a record.
What I *did* want and never got was a pony.
My family told me it was out of their reach, and I would have to save up the money myself. The magic number I was told was $100. (That may seem ridiculously low to you now, but to a 5 year old in 1959 it was astronomical)
It took me several years, but I did manage to do it. (Money I received as first communion gifts put me over the top.) At that point, I was told I would have to save up for stabling and food before I could buy a pony. No number was forthcoming.
Because I this, I have never had faith in any sort of contract what-so-ever.