But if you are asking what might cause your filament to break, I'd have to say if the tension exceeds your max tensile strength. this could be due to excessive tension or possible entanglement in your filament winding system.
Of course the filaments can break. Glass and Carbon filaments break very easy if they are bend around small radius of curvature, so you should plan the guiding elements very carefully if you plan to use such fibers (which I suppose, as you mention filament winding for composites). For the "normal" textile fibers this is not so bad, for such the Answer of Ali Amiri is correct :-)