I have also experienced that the initial
POST request works but but the following
PATCH requests fails with
AutomationPlansController in Sitecore.Marketing.Automation.Client uses AutomationPlanRepository to find the plan, and if it is not found 404 is returned.
The result is that if there is anything wrong with xConnect or SolR connection or schema, marketing definitions, etc., we will get this 404 error and there aren't really any usefull log entries.
I had errors in SolR and a custom computed field, I could see that in the Crawling log but not while this method failed. When the error was fixed I could repopulate SolR schema and depoloy market definitions, then the save and update operations worked.
Also note that those endpoints requires that you have runAllManagedModulesForAllRequests enabled in your web.config (we usually disable that for increased performance: