Think about it...
That ship could have just left after the bomb was on the corvette. No other fighter patrols were coming in, because the one that came back was destroyed.
Did the frigate stay to mop up fighters?
Because I think that ship could have just left as soon as the team was on and all the covenant fighters were destroyed no?
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We destroyed all the fighters; UNSC Savannah still had them. It should have undertaken evasion measures, whilst sending out small craft to target major weapons systems on the Corvette. Unfortunately, not every captain can be a Keyes.