I highly speculate that combinator SSS(SS)SS is not strongly normalizing. What is the argument for the non strong normalization?
Did you have a look at the second part of Johannes Waldmann's thesis The Combinator S ?
He proves that the normalization of S-based combinators is decidable and provides a procedure. SSS(SS)SS does not normalize.
He also refers to Dobouè's combinator S(SS)SSSS which does not normalize.