Wow, my first reaction to this was - change the needle. I find that is the cause of my thread breaking. Sorry that didn't work for you. Are you using the correct bobbin for the machine? I find that too makes a difference. I tried using a bobbin I have for another machine, but the Brother 400SE machine did NOT like that and the thread kept messing up. Went back to the correct bobbin and it works great.
Also, if you are trying to use thread on a cone, it can sometimes become to taut and breaks the thread. I bought one of those winder things that I can transfer my thread from cone to a spool... no more problems.
Good luck finding what is causing it - let us know, it might help others of us.