I've never heard of such a thing. Where did you hear this at?

Edit: Actually, now that I think about it, you're kind of forced to use a Limit Break when you get one, so it really wouldn't make much sense for them to become weaker the more you use it. Plus, it's supposed to be a help in big battles to deal some extra damage on your enemies.

I'll check my guide and some sites but I think your informer may be incorrect.