Is it that really thin clear stuff? Which type of beading are you doing? Some sort of bead weaving like peyote stitch with seed beads?
If you can pick a heavier tensile strength that will still pass through the beads, you could try that.
Some kinds of actual fishing line is made to degrade/break down after a while (environmentally friendly type deal), so it's better to get the stuff sold as actual beading material at a craft store. I have read that stuff like FireLine, Powerpro, and Spiderwire is good to use.
I do a lot of stuff with seed beads or delicas, and have awesome luck with this Silamide stuff. It isn't clear, but comes in a bunch of colors. It's sort of like Nymo (a nylon beading thread), but it is twisted and comes pre waxed. It doesn't wear or break as easily as Nymo; however, if you are using some sort of bead with holes or edges that are abrasive, you might be better trying something else. Those brands of fishing line I mentioned in the last paragraph might work for the abrasive stuff. Or look on the labels for a thread/line that has a core with some number of fibers, and is wrapped by others, or something with kevlar. Sometimes they will have labels that let you know what they are best used for- ie something abrasive resistant, or something with all around good tensile strength.
Good luck! I hope that gives you a hint in the right direction.