If your goal is to ensure only the legitimate sender with knowledge of $s_1$ and $s_2$ can answer the challenge, then this protocol fails to achieve your goal: eavesdropping a single challenge/response pair $(y, z)$ is enough to forge any number of subsequent responses pairs with the same $s_1$ and $s_2$.
Specifically, $z = y \oplus s_1 \oplus s_2$, so to forge the correct response $z' = x' \oplus s_2$ to a subsequent challenge $y' = x' \oplus s_1$ it suffices to recover $s_1 \oplus s_2 = z \oplus y$ and then to compute $$z' = y' \oplus s_1 \oplus s_2 = x' \oplus s_1 \oplus s_1 \oplus s_2 = x' \oplus s_2$$ as expected.
If each $x$ is independently uniformly distributed, then you can't recover $s_1$ or $s_2$ from it (effectively, you have encrypted $s_1$ with the one-time pad $x$ in this scenario!), but seldom is the pad the object you're interested in protecting in the end!
So what are you really trying to accomplish here?