This may happen by 2 reasons:
- Wrong transform controller.
- Activated locks in link hierarchy.
Select object and go to Command panel → Motion tab/panel → Assign Controllers rollout. Here check assign controllers for every transform operation and according to them manipulation tools (position, rotation, scale). Also expand and check their sub operations separate for X, Y and Z axis. Here, you need to assign right transform controllers for every manipulation operations and for every axis.
If "Position" item hasn't a "Position XYZ" controller assigned, then assign it. Select "Position" item and click "Assign Controller" button above list area and from controllers list choose "Position XYZ" and press "Make default" button below and "OK" button. Now you can see that "Position: Position XYZ" is already. Click plus sign (+) to expand list and, individually select X, Y and Z positions item, and for each one element also assign controller, but for them choose "Bezier Float" controller.
For "Rotation" item, do it also, like before. If controller assigned is not "Euler XYZ", assign this controller, but for each sub element (X, Y, Z) assign "Bezier Float" controller.
For "Scale" item, assign only "Bezier Scale" controller.
Locks in link hierarchy
Select object and go to Command panel → Hierarchy tab/panel → Locks rollout. Uncheck all items here, if they are checked.