Interesting topic...
Not taking into account children but adults:
The reason I find people moving away from more expensive web hosting companies to cheaper ones are often they cannot afford this extra pleasure; as face it, for a lot of people it is simply a pleasure, simply a personal site which wouldn't cost them anything if they didn't have it [It'd probably save them]. Living costs are going up - petrol, food, books, television and so forth. A lot of adults who move from expensive to cheap do so because they look at situation, and feel it's more important to buy food and other things which are a necessity as opposed to an extra which isn't really needed.
However, another reason I find, which is less common although does occur, is that the person does not need any support - However needs the server to be up. They then think going with a cheaper provider will be better as for them it does not matter about support, since they don't need it [In regards to setting up e-mails, etc.] however they just need the server to be up.
If I myself were the client. Well, I would if I received phone support. I don't spend big-money unless I'm able to call them up. Oh, and I don't mean phone support in the U.S., I actually mean phone support either here in France, or in Germany or in the U.K. [I don't mind an international call to the U.K. or Germany; however calling the U.S. just costs too much - Especially if I'll be on the phone for ten or twenty minutes]; oh, and they must be fluent in English.
