Open up the BrawlStick, unless if it’s still under warranty, and you want to contact Madcatz and fix it that way.
Otherwise, open it up with a screwdriver, and remove the two wires connected to the Y button with Quick Disconnects. Take those off, and peel back the vinyl sleeves.
Then, plug it into the system, touch the two metal tabs together, and see if the button will always work. If it does, it means your button is just bad. Replace with Sanwa or Seimitsu buttons to fix.
If it doesn’t, then it could be a PCB problem of sorts, but just try that to see first.