At what point can brass no longer be reloaded and what are the signs to determine when it is time to throw brass away?

Two main indicators, split necks and expanded primer pockets.

I have brass I've loaded 20 times.

It depends on the case design and how heavy the loads are:

1. Straight walled cases with low pressure loads will usually start splitting around the mouth of the case.

2. Straight walled cases with high pressure loads especially with a sloppy chamber may have head separations before splits around the mouth.

3. Bottle necked cases tend to have head separations.

4. Excessively large primer pockets would be seen with any high pressure loads after a number of reloadings. Sometimes though if the brass is soft, primer pockets even expand with lowish pressure.

Case mouth splits are easily detected on inspection. For primer pockets, when I seat a primer and it goes in a bit too loose, I mark that primer with a permanent marker and discard that case after that use.

You can detect incipient head separations by the shiny ring that forms around the case above the web or, better yet, by running a bent wired down the inside of the case to feel for the groove that forms before you get a complete head separation.

I load my brass in units. Each case in the unit is fired before I start over with it. When I get @10-15% neck splits or the primer pockets starts feeeling sloppy, I dump the whole unit in the brass bucket and prep up another batch. I don't count the number of times I've re-used brass 'cause I'm just not that sort of reloader but it will vary from rifle to rifle, cartridge to cartridge.

With bottleneck cases I've had very few case separations over the years, the necks always seem to go first.

In addition to what others have said, if they have been trimmed three times toss em.
If you don't be prepared to see some separate.

If you start with 300 cases, a new barrel and anneal the brass every 3 firings, you will wear out a few barrels with that same brass before you ever have to buy new ones!

Me and Mr Camuglia actually agreeing on something.... who'd a thunk it?
..
If you load brass were the load is in the 45,000 PSI range or less, and anneal every 3rd or 4th time, use a neck die to resize and a body die when needed, you can get a fairly long life span out of brass.. I have the web split a lot now before the neck, because the web is not being annealed. That comes from having to full length resize it too many times.

I did an experiment on a batch of 223 brass ( consisting of 10 pieces) and then a batch of 22.250 brass ( consisting of 10 pieces).

I reloaded them, annealing every 4th time and bumping the shoulder back every 8th time it seemed.

one the 22.250 brass, I quite at 40 reloads..

the 223 brass ( Rem Head Stamp, and was picked up free range brass), I reloaded those cases 100 times before I quit. there were 3 casualties along the way on the batch of 223 brass, however each one was not case failure, it was operator error on the load bench...

What motivated me to test them, was on Lapua's web site, they were indicating that they were getting 300 plus reloads on some of their brass in their ballistics lab....

so that made me wonder about how long one could make American brass last...

annealing, neck sizing, dedicating the brass to one rifle, and loading on a bolt action, and not pushing the brass to max velocity, Ie loading it hot..

it is surprising how long one can stretch the life of brass...

my other motivation was if the potential came that brass became hard to get due to some stupid democrat sponsored government regulation...