What determines whether a sherbet will set or not?

There are several things that keep frozen desserts (ice cream and sorbet, not just sherbet) from freezing into a block of ice. They're essentially all the ingredients besides water. If you have too little of these things, you'll have very hard ice cream; if you have too much, it might never get firm enough to scoop in your freezer.

• Fat - ice cream is the easiest to get soft, since it contains the most dairy, but this works on sherbet too. The more cream, the softer. But even butter freezes hard, so this isn't going to keep it from setting.

• Sugar - this is pretty easy to vary in all frozen desserts. It'll have a noticeable effect on softness, but reasonable quantities won't make it too soft.

• Alcohol - obviously you won't always want to use this, but the right alcohol often goes very nicely with sorbets. Enough alcohol would of course keep it from setting, but it takes a lot. A sorbet made from wine, sugar, and strawberries still sets, though it's quite soft.

• Air - this gives the dessert a softer, fluffier texture, but of course won't ever stop it from freezing. Make sure to churn things long enough, though you can only ever do as well as your ice cream machine lets you.

• Additives - gelatin is the main one that's common in kitchens; guar gum, and xantham gum are next up. There are also various stabilizers for keeping ice cream smooth.

I don't think I've ever seen a recipe for a frozen dessert that wouldn't set at all. It takes an awful lot of fat, sugar, or alcohol just to get it too soft. My best guess in the case of what you saw on TV is that she either went overboard with some kind of additive, or didn't manage to properly freeze it. Note that with home ice cream makers, things will be at least a bit too soft coming straight out of the machine - but they'll set much harder in the freezer.

In practice, if you're making your own, the problem you'll reliably have (especially with random recipes online) is that it's too hard. Storebought frozen desserts if anything tend to have more sugar and fat than you'd use at home, and often have additives to soften and stabilize on top of that. So most things you make at home will tend to be harder than what you buy in the store.

Credit where it's due: I learned some of this from the introduction to The Perfect Scoop by David Lebovitz; a lot of similar information is available in this post on the author's blog.

What might be at issue is the specific gravity of the mixture. That is to say the ratio of sugar to water in a sorbet but also similar in other frozen desserts.

If you have too much of one and not the other the mixture will either freeze rock hard or need a much lower temp to obtain the desired solidity.

I found a reference from a website about creating an easy hydrometer using an egg that will let you know about where you stand (it works quite well). It's very useful to test your mixture especially if making a sorbet that has alcohol in it as that really messes with the way it will turn out. Make sure the egg has been cleaned well. Alternatively go buy yourself a proper hydrometer.

Here’s an old-fashioned trick that will help you get the right balance of sugar to liquid: Float a washed, uncooked egg (still in its shell) in the liquid; if the part that shows above the surface is the size of a dime, the sugar concentration is right; if it’s larger than a dime, the sugar content is too high. In effect, you’ve got a homemade hydrometer, which measures the specific gravity of the liquid. This is very useful when making sorbets with fresh fruit, since there’s no easy way of knowing the fruit’s original sugar content.

Hope this helps.