What the title says. After traveling over 30mph for a minute or so, the engine suddenly wants to die when I hit the brakes. I checked for vacuum leaks with carb cleaner, and there aren't any (although someone cut out a lot of the vacuum lines in the past). Sometimes when the engine dies after this it really doesn't want to start back up, and I have to feather the pedal just to keep it running. It has power brakes, with one vacuum line leading into the #6 intake tube. Kinda need this car to be reliable as my daily is now having a lot of issues.

I would suspect a leak in the brake booster just based on the info you provided, but I really have no experience with power brakes on these cars.

What's the year and model?

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Somehow I ended up owning three 1964 slant six A-bodies. I race one of them.
Escape Velocity Racing

1975 Duster.

If no power brakes:

Braking also causes fuel to slosh forward in fuel bowl. If fuel pump is under performing, and or float incorrectly set or fuel logged, result would be low fuel level in bowl, slosh action could leave jet high and dry momentarily.

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67' Dart GT Convertible; the old Chrysler Corp.
82' LeBaron Convertible; the new Chrysler Corp
07' 300 C AWD; Now by Fiat, the old new Chrysler LLC