Docker container in QA/Production

We are new to Docker and Containers but have been able to get a couple of containers up and running with a aspnet core site with node js and another with a microservice.

I have docker desktop running on the machine that builds and deploys the containers for a QA version of the site.

One thing I notice is that Docker Desktop seems to stop running or only runs on a login so if a login is timeout, it seems like docker desktop stops running and my container build / run process fails.

Is there a way to keep docker desktop running all the time?

Can we use docker desktop for a simple application / service in a Production environment?