I saw one video by the Star Wars Reading Club about this, and it made me wonder as well why Grievous never helped Dooku out during the battle between Darth Tyranus, Anakin Sywalker, and Obi-Wan Kenobi. Considering that Dooku trained Grievous, he should have been more worried about his apprentice.
Is there any official explanation by the novelization on why the General didn't help the Sith Lord between the two Jedi?
According to the film's official novelisation, Dooku ordered Grievous not to intervene.
Dooku was, in turn, acting on orders from Palpatine who (unbeknownst to Grievous) was trying to provoke a duel between Anakin and Dooku.
Dooku turned. From his commanding height, he stared down at the blue-scanned holoimage of Invisible Hand’s commander. “Your objections have been noted already, General. Leave the Jedi to me.”
“But driving them to you also sends them directly toward the Chancellor himself. Why does he remain on this ship at all? He should be hidden. He should be guarded. We should have had him outsystem hours ago!”
“Matters are so,” Count Dooku said, “because Lord Sidious wishes them so; should you desire to press your objections, please feel at liberty to take them up with him.”
“I, ah, don’t believe that will be necessary …”
“Very well, then. Confine your efforts to preventing support troops from boarding. Without their pet clones to back them up, no Jedi is a danger to me.”
The deck shuddered again, more sharply, followed by a sudden shift in the vector of the cruiser’s artificial gravity that would have sent a lesser man stumbling; with the Force to maintain the dignified solidity of his posture, the effect on Dooku was confined to the lift of one eyebrow. “And may I suggest that you devote some attention to protecting this ship? Having it destroyed with both you and me aboard might put something of a cramp in the war effort, don’t you think?”
“It is already being done, my lord. Does my lord wish to observe the progress of the Jedi? I can feed the security monitors onto this channel.”
“Thank you, General. That will be welcome.”
“Gracious as ever, my lord. Grievous out.”
