It depends on the calibre you're reloading, the availability of cases an a multitude of other factors.
If you were, for example reloading 30.06, you can usually pick up a few hundred cases at the range on a given day. 240 Weatherby Magnum cases are a different story
I only reload once and toss them, since I reload 270, both the 30.06 case and 270 cases can be used and so readily available.
What calibre are you reloading, and what loads are you using ?

You should be able to get several accurate reloads out of a case. I typically keep using the brass as long as I can until I start to notice it's approaching wear-out. Look for signs such as firing residue seeping out from the primer /primer pocket edges, primer pocket more loose and primers not seating as tight as before, bullets seating too easy once case has been resized, case wall area forward of the case head wearing thin (can be checked by running the tip of a paper clip inside the case and feeling how much indentation there is on the inside near this area). Once I begin to see these signs I smash the case with a pair of pliers and scrap them.

Good cases loaded properly should give you several reloads out of it. Just don't wait until a neck splits to discard the case. Scrap it before it happens. A split neck can have will have a negative affect on your accuracy for that particular shot.

I'm loading IMR 4895-43-45g (seeing what does best), 168gr Matchking. I have no chronograph yet. I'm told to keep it down a little for my Browning Bar.
Frontiersman

You mentioned accuracy. That's a relative thing. In a match rifle 1/2" is a worn out barrel and will win no matches. In a hunting rifle, 2" is fine at reasonable ranges.

Two things are going to wear out your cases; pressure and work hardening in resizing. In the first case, you'll notice the things westernhunter mentioned. Primers starting to leak and seat to easily and streaching of the case in front of the case head. I might add to watching for streaching, befor the case seperates, you should notice a bright ring in front of the head. Your seeing where the case is getting thin and ready to seperate. If that ring appears after only a fireing or two, with standard cases, you should have the headspace in the chamber checked. That ring is usually seem in belted magnum cases that head space on the belt. In unbelted rimless or rebated rim cases you won't see it unless there is excessive headspace. The reason being that those cases headspace on the shoulder.

Even with mild loads, cases will fail in the neck due to caseharding durning reloading. Then you'll see necks start to split. The cure is anealling the shoulder and neck. I've found that it's best to just discard cases by then. If your shooting full loads, your primer pockets are probally getting loose anyway and cases for most standard cases, especially those based on the 30-06 and 308 are just to cheap to justify anealing. If your not shooting full loads, cases are still to cheap to mess with.

To help slow down case hardening, partial resize every other loading. Back out the sizing die a couple turns and run a lubed case into it. Take out the case and look at the sizing marks on the neck. A little at a time screw the die back in until the marks are just barely off the junction of the neck and the shoulder. Run the case thru your chamber and make sure it works well. I full length resize all the time as I have hunting rifles and a better case fit in the chamber is of little value to me. What I need are cases that feed EVERY TIME! And as I said eariler, cases are cheap.

The only time I've noticed a considerable accuracy difference is when the neck is starting to wear out. If the necks look good and a given batch of brass has not had a blown neck in its ranks, I tend to just keep using them....

For big game hunting, as long as the brass is not near failure, I don't think brass wear is a big issue. Match and long range varminting is another story though....

the cases I have had fail have been about 1/2 in up from the bottom or primer end. The cases basically cut in half. I have not noticed or had trouble with the neck end. Although I have not reloaded for years and am now digging my stuff out and setting up. the case breaking off like is a fear as the end can stuck in the rifle. I only use new or first time reloads while hunting, so I have had only trouble at the range and the wire cleaner took out the piece. In your opions is this making the round to hot, crappy cases, or just basic case fatigue. these have been reloaded factory stuff and not sure of brand.