In addition to Pete's excellent answer as a way to "diagnose" the problem I would suggest fingering the note G and watching the body octave pad as you press the thumb key. It should raise without sticking or hesitation. Next with the octave key still pressed use your free hand to close the body octave pad with your finger to feel the spring tension. If it feels weak, that could be a part of the problem. Finally while fingering G with the thumb key, raise your 3rd finger to go from G to A and back. The body and neck octave pads should exchange places as you do this. To check if there are any bent keys or rods that are creating friction in the octave mechanism, remove the neck and while fingering A and pressing the thumb key, use your free hand to move the rod that extends from the saxophone to engage the neck "ring" up and down. It should "float freely". If note something needs to be straightened or cleaned and lubricated.