How do I reconnect to docker-compose live log after docker container start?

I used docker compose to set up a container group. I use docker container stop to shut them down so I can start them up using docker container start from a ps file in order to speed things up. By doing this, however, I lose the live log, which is helpful. Is there any way to reconnect to the all/each of the containers’ output in one window from the same ps (powershell batch) file?

Not sure if I understand your question correctly, but if you mean you want to tail your logs you can do docker-compose logs. You can add -f to keep it running. Optionally you can specify a container name, otherwise you will se logs from all containers.