How wouldn't it? The ongoing coin-days staked in that fork specifically is what allows it to continue making forward progress. Just like how in a PoW fork, the ongoing consumption of energy in that specific fork is what determines the security of that fork.
The argument you link in that other thread is interesting but it doesn't appear to be exactly what you are talking about. They seem to be describing an attack where nodes are taken offline by the attacker.
Coin-days staked has no bearing on a pure PoS chain’s risk of being 51% attacked, nor does it have any bearing on the risk 1/3 or more of its validators get disrupted. Not so with PoW hashrate: enormous hashrate imbalances between forked PoW chains directly translate into decreased data immutability per the risk of deep chain reorgs.
Those risks are simply not present in the PoS corollary.
To use a real world example, Bitcoin PoW mining consumes in excess of 100 Terawatt hours of electricity per year. If Bitcoin were to undergo a repeat of 2016 today, and the Bcash blockchain were to be serviced by miners consuming less than 10% of the energy spend of the incumbent (Bitcoin), Bcash could be easily 51% attacked.
But in the PoS corollary to Bitcoin v Bcash, coin-days staked would have no bearing on Bcash’s ability to continue making forward progress. Just so long as it remained difficult to either disrupt 1/3 of Bcash validators or acquire 51% of it, Bcash would continue functioning perfectly well (see: Jude C. Nelson [1]). At that point the rightful heir to the Bitcoin title would have to be determined socially. It could not be determined without top-down human intervention.
[1]: https://news.ycombinator.com/item?id=26810619