Yeah primer bulbs go after a while, they have a one way valve in them that eventually breaks. They are cheap. Also it's agood idea to try and install it in a vertical position, as it helps the one way check valve work better.
If it's not getting hard, and it always should, then it could either be the bulb itself or other fuel system issues, like as was mentioned about a filter problem or fuel pump problem, but more than likely it's a carb issue.
First thing I would do is replace the bulb and see if it is the problem, if it still doesn't get hard you could have a carburator needle not seating, meaning it is stuck open and flooding one of the carbs, that would be my first look if the bulb is not the problem.