Jira comes with a default "Start date" locked field. However, it is still possible to create a new unrelated custom field called "Start Date" (capitalisation of "D" letter). 

If creating aforementioned custom field and attempting to change the value of the "Start Date" field in Automation, this can result in failure of the rule to successfully modify the value of the field. 

For example, if triggering a rule on a sub-task and then creating a Branch to manipulate the Parent, a Then rule could attempt to change a field of the Parent like so: 

subtasks.Start Date.max

Attempting to manipulate the new custom field "Start Date" does not result in any change to the value. 

Workaround. 

Rename the "Start Date" custom field to any other value. Even putting an underscore like "Start_Date" should fix the problem.