Is one time pad cipher reuse and random key secure? The sender and receiver share two different secret keys:  s1 and s2 both y bit values. 'x' is a randomly generated y bit value. The reader sends to the tag a challenge y =  x ⊕ s1, and the receiver  responds with z = x ⊕ s2 after recovering x = y ⊕ s1. 

s1 and s2 never change, x is randomly generated each complete transaction.
Can you determine s1 and s2 through a single transaction? After multiple?
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?