Inline Edit is not Available for a Specific Object

To resolve the issue, check whether the Edit button for the affected object has been overridden with a Visualforce page. When the Edit button is overridden without setting inlineEdit='true' in the apex:detail component, Inline Editing is disabled for that object.

To determine this:

Classic Setup:

For standard objects: Go to Setup | Customize | <Object> | Buttons, Links, and Actions, and note the "Overridden" checkbox next to the 'Edit' standard button.
For custom objects: Go to Setup | Create | Objects | <Object>, scroll down to the Buttons, Links, and Actions section, and note the "Overridden" checkbox next to the 'Edit' standard button.

Lightning Experience Setup:

Setup | Object Manager | <Object> | Buttons, Links, and Actions | and then see if the Overridden column for "Edit" standard button is checked.

The Visualforce Page overriding the Edit Button must specify inlineEdit="true" within the <apex:detail>.

Important Note

If the Edit action has been overridden for an object, Inline Editing may not be available for that object in either the record detail, related record or (dynamic form) field section components.