First, if you have 55 nights, you've already earned 2 suite upgrade awards as you get 2 at 50 nights, another 2 at 60, and 1 for each additional 10 nights up to 100. They are Milestone Rewards and not tied to status.
It generally takes a day or two for a stay to post after you check out. Assuming you met a threshold, the award should post at the same time. In your scenario, you would not have an upgrade in time for your second stay.
Oh whoops, sorry, I mixed up my milestone awards
that is good to know! Do you think if you called Hyatts Concierge team they might be able to get the certificate in your account faster manually?