Please be careful about mentioning real life examples as they tend to distract from the question. Historical examples of states reaching their manpower limits would be useful though.
There's a lot to consider in this question. Some thoughts I've had to bring it together:
- Each state has a limited pool of available manpower, which according to Wikipedia's List of global manpower fit for military service, seems to be roughly 15% of the total population. I'm using just men here since most countries don't allow women in front line combat. I'm using a big assumption that the majority of soldier casualties will be combat units.
- Modern armies have a tooth to tail ratio that means each combat soldier needs so many support personnel to be effective. It appears this is around 15% of the total manpower mentioned above.
- This does not include how a state's available firepower and hardware affects that ratio. e.g. It's difficult for a state to make advances without armoured vehicles, but they can hold their positions without them.
- A defending country can of course keep fighting a guerrilla/insurgent war even when the enemy has won by most accounts but I would like to scope this question purely to the ability for that state to coordinate, attack and defend in a conventional combined arms war on multiple fronts and maintain or move the frontlines.
- Less soldiers can be just as effective as more soldiers on a smaller front, but there must still be a limit. Like 5 soldiers cannot be used as a modern combined arms army. So there is a very rough minimum number somewhere.
- Economy doesn't come into play here because you can have a great economy but if you no longer have anyone to fight the war, you've lost. The reverse can be said too, but in this question we're focusing on manpower losses only.
Also "casualties" may be a bit ambiguous since an injured soldier could return to the front line. Perhaps it might be best to say "no longer able to serve as a combat soldier". After all even if they are moved to support, the "tooth-to_tail" ratio will shift. I don't know what ratio of recorded casualties, on average, generally become permanent.
I'm looking for answer that assesses the variables involved that add up to a state maintaining it's strategic cohesion while sustaining losses in manpower, or rather adding those up and trying to estimate the limit. e.g. "Considering [n variables], adding them together it seems a modern state could perhaps maintain losses of up to 40-50% of its manpower before it's ability to wage a modern war collapses"
Or to put it better: A state will lose all strategic cohesion if it loses 100% of it's manpower. This is true. However it will also lose that if the state loses 99% of it's manpower. There won't be enough in the military to even call it one or tackle a modern opposing force. So how much do we continue to reduce that percentage until it is effective? Until a hierarchy can coordinate a modern combined arms defense or offense against another modern foe?