Brake Problem

Have a 96 coupe with a brake problem that just appeared. My brake paddle started to feel odd at first and then they went out completely. Brake Pressure light came on. My fluid reservoir was a little low but below the
low level. Around the reservoir cap it was wet like fluid was leaking out (which it was). Went and bought a generic cap at the local auto store and replaced the old one and added fluid. Went for a test drive and the brakes were still weak but they returned to normal after a few stops. Did some hard stopping and everything seem to be back to normal. Head back home and as I'm pulling into the garage the brakes go out again (pedal down to the floor without any resistance. Notice that around the cap fluid was leaking again even with the new cap.
Wondering if the problem is with the cap or if the cap is designed to allow for fluid to escape at a certain pressure level???
Thanks for any advice anybody can provide.

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