Tangentially I was looking at Render.com the other day and they also don't support zero downtime deployments if you have a mounted volume, so it's not very uncommon even on cloud platforms.
As for restarts, I didn't have that problem yet, I believe CapRover adds `restart: always` to all the running containers so they should automatically boot. You might want to check out the logs of the containers that don't restart or just always hard restart the server after a Docker update.