The problem is related to a similar question about lambda calculus.
This question is about SKI combinatory calculus. I want to find a term $M$ without a normal form that will yield a term with a normal form after application with the $S$ combinator: $$(M S)\text{ should reduce to a normal form}$$
Since every term of lambda calculus can be translated to a SKI term, one can also assume that $M$ is a lambda calculus term.
For example: If the right hand side of the application was the $K$ combinator, one can construct $M$ using the translation of the lambda calculus term $\lambda x.((x I) \Omega)$, where $(K I)$ will then result in $\lambda x.\lambda y.y$, and therefore $((K I)\Omega)$ yields $I$.
I was not able to find a similar example for the $S$ combinator (or $I$, but I mainly care about $S$). Can such a term even exist and if not, why?
Okay, I found an answer. I definitely didn't think about the problem long enough, sorry. Maybe this helps someone else though.
Let $M=\lambda x.((((x I) I) \lambda x.\lambda y.I) \Omega)$, then $((SI)I)\leadsto\omega$ and $(\omega\lambda x.\lambda y.I)\leadsto\lambda x.I$. Now we have the same situation as the example in my question, ultimately reducing the term to $I$.