MICKEY 2.0: Mutual irregular clocking, register states
In any keystream generator, if the state repeats, so does the keystream; which, under some standards assumptions, can be detected, and leads to a serious break (e.g. if the beginning of the plaintext is known for length a little above $k+\log_2k$ bits, where $k$ is the period of the keystream, then the period $k$ and the rest of the plaintext can be found). A necessary condition for security is thus that odds of the state repeating are negligibly low. This is insured (odds are zero) if the quoted property holds:


  ... the state of the generator does not repeat within the generation of a single keystream sequence ...


and that's why that property is desirable: it insures there is no class of weak keys leading to attack.

I'm not seeing assertion in the article, or simple proof, that “the state of S does not repeat within the generation of a single keystream sequence”. Rather, I see the reasonable assertion, without formal proof, that starting from a generator S based on iterating a lossless function, and using another unrelated generator R as an excitation to S by a combination with XOR keeping the iterated function lossless, it seems unlikely that the resulting generator S' ends up having a period shorter than R (that could occur only for a limited number of R having some sort of tight relation to S; perhaps that's even demonstrable). Rather, it is expected (in the absence of feedback of S to R, and if the function used in S is random enough) that S' has period a large multiple of the period of R, with the large factor commensurate to the square root of the number of possible states for S.