I have a small 3 foot whoopie in my emergency kit and if I wear a belt I wear a Dutch clip and webbing belt.
I typically carry an extra 12' or so of suspension grade cord. I've needed it on occasion to extend the reach of a tree hugger to get around a fat tree. Enough to repair a busted cord on one end of the hammock easily, if needed.
(alias ProfessorHammock on youtube)
No spare suspension here, just some spare cordage.
If you think you might need it, take it.
It will give you an option if needed. And a sense of security.
Ambulo tua ambulo.
Most suspension systems are robust enough to not worry about them being the point of failure. I do carry two 6' suspension extenders (Amsteel with an eye spliced in each end) and Zing-It 1.75mm (~500#) bear bag line.
Hey thanks for the input everyone. I was planning on just taking some extra cordage with me. I always carry a lot of cordage and I know enough knots to make due if something were to happen to my hammock suspenion.