Okay, in Twin Shadows there's a mission where Threepio can be deactivated by getting shot up by the bad guys, but then the heroes can reactivate him.

Okay, so here's a very likely scenario:

On the Rebel turn they activate Threepio first, to focus somebody or something, then the Imperials go and blast Threepio first chance they get. Then a Rebel hero interacts with Threepio and reactivates him.

Can he then be used again to maybe focus someone else, all within the same round?

Answer your question with a question:

When the rebels activate Threepio, does his deployment card ready if it is already exhausted?

When the rebels activate Threepio, does his deployment card ready if it is already exhausted?

No it doesn't. Relevant snippet from the mission briefing:

At the stat of the mission C-3PO is deactivated. While C-3PO is deactivated, he is a neutral figure but does not block line of sight.

A Rebel figure can interact with C-3PO to make him operational. While C-3PO is operational, he is a Rebel figure and heroes control him as an ally. If C-3PO is defeated, his figure remains on the map. He discards all conditions and damage tokens and becomes deactivated.

There is nothing in there to suggest that C-3PO readies when he is woken up. What I would do is to place a strain token on C-3PO once he is deactivated and otherwise treat him as a normal ally. So if the Rebels wake him up twice in a round, they don't get free actions out of him.

Agreed. Activating C-3PO only give the Rebels control over him as an ally, it does not ready his deployment card.

Thanks.