Strong beading string?

[moonflake.livejournal.com]

I've tried to search for this in beading sites and such but all I seem to find are instructions on beading the pearls, not so much about choosing materials.

I made a cellphone charm and a necklace recently with beads using illusion cord or some such. The knot on the necklace slowly came loose, and so the whole thing broke. Wisened from this, I used nailpolish to seal the knot on the cellphone charm, but this time our kitty dropped the phone and the cord broke at a point near the knot. So I'm not entirely convinced I should be using this cord at all. But what would be a good, endurable string/cord to use for such projects? I'm afraid that with wire they'll seem too stiff.