If you start a deployment ("your container", roughly speaking), the age of that deployment will keep counting up even if the container exits-- k8s restarts it of course-- and even if the k8s scheduler goes down-- since we want to be able to restart the scheduler without unnecessary service restarts.
At home, it's all on one computer in my basement, so when I reboot that box, the k8s reports come back and keep telling me the deployment has been there for xx days (just with some availability hiccups).