I'm afraid not. You could have kept your colleague for the remainder of her term of office, but I don't think a resignation can be withdrawn so long after the event. In any case, there might not be much left of that term.
It's a pity she did not feel able to stand for election, although it is not an easy job representing such a diverse range of people.
Serving co-opted governors were all allowed to finish their term and, though it would have meant missing the first chance to stand for electon, many did just that and the school benefited for a while.
I personally regret that the law removed the freedom of the governing body to co-opt school employees. I know it was a response to complaints in some areas that by one means or another too many people who owed their livelihood to the school were finding their way onto the governing body and unbalancing representation.
But I think the question of balance is best left to governors themselves, who have the means to correct that balance in their own hands.
I know this isn't the full answer, but remember that if the person you speak of has some valuable expertise within the school - on finance, say, or special needs - there is no reason why you cannot invite her as a visitor to meetings when such items come up. You can even co-opt her onto an appropriate committee, if the whole governing body agrees.