That depends on many variables. Some rifles show case head separations after only one shot, while bench rest shooters expect the cases to last the life of the barrel. Two key things come into play though. One is annealing; this is a process in which the neck, shoulder, and upper portion of the body are made soft. The softer the brass starts out, the more you will be able to work it before it becomes brittle, and the necks start to split. If cases are really hard to come by, it is common practice to re-anneal the cases, thus allowing many more shots to be fired before the case becomes useless.
The other thing that comes into play is how hard you work the brass. If you're shooting the brass in a gun that allows the brass to stretch (ie: a rear-locking Lee Endfield), or you're full length sizing the cases after every shot, then the cases will be allowed to stretch as though they are being fired in the gun for the first time, thinning the brass at the expansion ring, resulting in a case head separation after only a few firings. If you where to partial size, or neck size only in a strong, front locking firearm, then you cases should last many shots. There are many exceptions to this though; one being, if your chamber is out of round, or the dies are ill fitting, these situations will over work the brass as well.
In saying that, those are some of the things which make reloading fun.
Mike