As you mentioned, looks like there is some kind of scheduled automated maintenance batch process is in place. Which stops the publishing process.
So I would suggest first check if there is any Scheduled Automated Script, and if it there how it's stopping/starting the services. Looks like, while stopping/re-starting the publishing process the script is not doing it in a proper way.
One such case I can thinkguess of is a "Clean UPUp Script" of temporary items during publishing process.:
As, we have a lots of intermediate files(stored in temp/Incoming folders) during publishing process and in some cases when anything goes wrong during the process the files remains there forever.
So to clean up those files by a automated script, the publishing process needs to be stopped first and a then re-start after clean up of files. I guess, while stopping/re-starting the publishing process the script is not doing it in a proper way.
So I would suggest first check if there is any Scheduled Automated Script, and if it there how it's stopping/starting the services.