Gw44,
That's not annealing, so it's a little OT, but it's good advice for hard brass fired in semi-autos or any other chambers that stretch the head a lot at each firing, so the pressure ring gets very thin. Tossing it lets you avoid head separations. But annealing is concerned with neck splits and shoulder working, so it's a different part of the case. Most brass will reload about a dozen times without neck splits, IME, but if you have a loose chamber neck, it can happen sooner.
At the other extreme, board member Hummer70, a two-time National Palma Match champion, has one .308 Winchester case he's succeeded in loading and firing 150 times. So much more life is possible with careful minimal resizing and periodic neck and shoulder annealing.
Prof Young,
To combine a couple of the previous answers, annealing brass is a reordering of the atomic structure of the metal to remove stresses and, with still more heat, thereafter to go on to lower its tensile strength and hardness.
Fully annealed brass is so soft you can bend it easily with your thumbnail and the necks can be easily bent off-axis when a round goes up the feed ramp. Full softness in the neck and shoulder is just too soft for shooting and is not desirable. What shooters do to anneal case necks is what is called "partial annealing" or "stress relieving" in the copper alloy industry references I've found. It is heating just enough to relieve stress, but no further, as stress relief (reversing work-hardening) is all that is required for the case to continue to withstand reloading operations.
Below is a graph of what happens to the brass at different temperatures over a one-hour soak. Shooters use higher temperatures so it happens faster. As near as I can tell from reading, the rate doubling every 10°C like a chemical reaction applies to stress-relief, and the second image follows that rule to show how much faster stress-relief occurs at higher temperatures. Mind you, this assumes the listed temperatures are reached in the neck and shoulder brass through-and-through.