By center brace, do you mean a vertical brace, or just across the top horizontally? If you're talking about a vertical brace then I think using .50 acrylic would be borderline safe. (for two four foot spans)
Doing it horizontally, my opinion is that .50 would be too thin.
The frame will have a lot to do with the safety factor too. If you're going to use thin enough acrylic that it'll depend on the strength of the frame, then that frame must be solid. If you go with thick enough acrylic it'll add structural reinforcement itself.
Another issue I would consider, the smaller the sealing surface versus the amount of bowing that will be going on. Thinner acrylic will bow more, which will put more stress on its seals, and the thinner the seals (like the 2inches or less that you'll have) the higher chance of one failing.