Mine live for milliseconds, but I'm a weird case where that's intentional as a security construct.
But that doesn't really have anything to do with the logging architecture. How long the thing lives doesn't matter when you're using aggregation, bypassing the local filesystem, and inspecting through a central portal.
People have been doing this in VM environments for a lot longer than they've been using containers. Whole companies and services were born to facilitate this, and some have even died already, in the time before containers hit full stride in the hype cycle.
Yes, I was left scratching my head as to why containers play any significant role in the issue of distributed logging. If your choice of container runtime/vm/servers are creating an issue with logging then there's most likely an issue with the system architecture rather than actual logging.
We've been building distributed systems (with containers and other approaches) for years and this is the first time I've heard of logging being a problem.