One reason you may want to constrain access to constructors is if you want to control creation of the object. An example of this would be the Singleton
pattern. If you search google for it, you will find lots of descriptions, along with heated debate about it's usefulness!
I realised that I didn't answer your question directly. A protected constructor is only available to the class and it's subclasses. So, this could be used in a situation where you want the subclass to have control over initialisation, while restricting instantiation of the base type.
E.g.
[ February 28, 2005: Message edited by: Horatio Westock ]