Do you have Mids' or are you using a Mac?
Shield Defense is just as survivable on a Brute as a Scrapper, and can be almost the same as a Tanker's survivability. Getting to 45% defense is the key. Without set bonuses, it is easiest to aim for at least 32.5% defense to all positions and use a small inspiration before the tougher fights. A tray full of them can last you 20 minutes, and that's without combining to make more as you go.
You are missing Weave, which is the most important toggle for just about everyone to take. It adds the most defense out of any pool power, and you pick up Tough to get it. Tough also adds a lot to your survivability because most damage is Smashing or Lethal. Those two powers alone should help immensely. Use your second or third build to pick them up if you can't afford a respec. Plan your build out in Mids if you can so you know what to take at each level.
I agree with Syntax 100%.
You could likely ditch both Leadership powers and one of your attacks to pick up boxing, tough, and weave (I would likely cut Chop). You could ditch 2 attacks if you plan to take ice blast.
If you could give some idea of your slotting, you might get more suggestions as well.
Active Defense probably only needs 2 recharge slots now that you're 40+. I would also pull a couple of slots out of Grant Cover. You can make them up later (or not). Against all odds really only benefits from end redux, and one is probably enough.
Download Mids' hero/villain designer if you don't have it, and poke around a bit in it. You should be able to come up with a relatively cheap build.
I have a level 41 axe/shield brute which does not seem to be doing very well. Dying once a mission at least is very common, and it just feels like I would have done much better if I was a tank, or a scrapper.
Her current build is as follows.