Create Recurring Series of Tasks Checkbox is Grayed Out or Unavailable When Editing or Creating Salesforce Task Records

Create Recurring Task Using Global or Custom Actions in Lightning and Classic

In order for the 'Create Recurring Series of Tasks' checkbox to display during the Task creation process, the 'Delete Series' and 'View Series' actions must be added to the Mobile & Lightning Action section of the page.  For more information on adding these actions to the desired page layout, see this article or visit the Salesforce Support video.

Since it isn't possible to add these buttons to an Action layout, it is not possible to display 'Create Recurring Series of Tasks' on the Action layout. 

Users can vote for Creating recurring tasks with a New Task quick action.

Checkbox for Recurring Task is Grayed Out When Editing an Existing Task

This is expected behavior. The checkbox for recurring tasks can only be selected when you are creating a new Task.

Users can vote for Creating Recurring Tasks by Editing Existing Tasks.