Non-interactive proof that an element is in a subgroup
My guess would be that they have a proof that their scheme has the zero-knowledge property if the challenge comes from the set $\{0,1\}$, whereas the proof doesn't work if the challenge comes from the set $\{0,1,2,\dots,2^{160}-1\}$ -- and they don't know how to construct an alternate proof to show the latter.

If you want to understand why their proof doesn't work for larger challenges, you should start by reading through their proof for small challenges and see if each step remains valid for large challenges.

For instance, you might find there is a rewinding step that works if the challenge comes from the space $\{0,1\}$ but doesn't work if there is a large challenge space.  This is a common phenomenom in rewinding-based proofs.  If the challenge space is $\{0,1\}$, you can rewind the challenger and run the protocol forward, and with probability $1/2$ the resulting challenge will match what you want it to be.  Thus, on average, you only need to try twice, and that's fine.   In contrast, if you used a random 160-bit challenge, the probability of success on rewinding would be only $1/2^{160}$, so you'd need to try $2^{160}$ times, which is not feasible.  As result, many rewinding proofs work fine if you have a 1-bit challenge but fall apart if you have a 160-bit challenge.  This poses a barrier to proving the zero-knowledge property using large challenges, using this kind of proof technique.  If the only way they know to prove the zero-knowledge property is using this sort of rewinding proof technique, then that'd explain why they propose a 1-bit challenge.