I had some invisible thread and now I can't find it. No, really, that's true. But I chuckle about it, because I figure the reason I can't find it is because -- it's invisible!
If you use invisible thread, don't use the nylon invisible thread. That is the stuff that deteriorates and breaks over time.
Instead, use polyester invisible thread. It will outlive you while still feeling supple and soft.
YLI, Superior -- and Coats & Clarks -- all make polyester invisible thread. And in my heart of hearts, I doubt any one is better than the other.