Similarly: yes, indeed, if your company continues interacting with PG and other Y-Combinator-funded companies, then it will not die -- because if it dies, it will no longer be able to have those interactions.
But that's false. People don't lose the ability to email us once their company dies.
The companies no longer have that ability, even though the individuals do.
Don't get me wrong; I think "keep doing something and stay in touch" is an excellent piece of advice for someone doing something difficult where failure is strongly correlated with losing motivation.
But I wonder whether you're overestimating the causal role of demotivation here. Toy model: a startup has some kind of "health score" which varies according to exogenous events; "motivation" is some function of health and d(health)/dt, which is small when the startup is unhealthy and getting healthier; the startup dies if its health goes negative. In this model, motivation has no causal role, it's a pure epiphenomenon; but I bet you'll find that startups that die typically have very poor motivation shortly before their demise, and that poor motivation is a good short-term predictor of failure.
Of course, this is only a ridiculous toy model; in reality motivation clearly does have causal effects of its own, but it's also clearly affected by outside causes that themselves have an effect on the success of a startup. An observed correlation between demotivation and death is only weak evidence that demotivation is the underlying problem more than it's a symptom of having no customers, no money, technical problems you can't solve, etc.
(Doubtless you have more evidence than that correlation, having seen lots of startups succeed and fail.)
But that's false. People don't lose the ability to email us once their company dies.